Leadfoot
Try working out your harmonies with a VST synth. Then take out the root note, and sing along with just the harmony notes. You can track your harmonies using this technique, then just delete the synth when you're done tracking the vocals.

A variation on this theme...I do the same thing, but with Melodyne. I create a harmony by applying Melodyne to the original vocal part, then learn the harmony, sing along with it, and eventually erase  it. (Interestingly, I'm often able to hit notes I didn't think I could reach when singing along with the harmony.)
 
And as jpetersen points out...
 

jpetersen
That said, if it's far back enough and there's a lot of other stuff going on, you can get away with it. What I find with Melodyne is that, if you shift a lot (a few tones) you get odd artifacts. But if it's pushed back, the character is still recognizable, so it will still sound like it's you singing.

 
This can indeed work well within the constraints he mentions, especially if you have Melodyne Editor and vary the formant (which you can also do with V-Vocal).
 

I mostly follow what many posters have suggested...I write all the melody and harmony parts to midi tracks - one track per part - and then play the specific part I am recording voice for along when I sing. I record the main melody line first, then tweak it with Melodyne and otherwise get it in good shape, then mute the midi lead vocal, but play the sung lead vocal along with midi harmony_part_1 while I sing harmony_part_1...Then Melodyne and fix harmony_part_1 and mute midi harmony_part_1 and move onto harmony_part_2 etc.etc.etc...
 
If I am singing high harmony parts, sometimes I will not try to sing the highest notes that are up out of my range, but rather repeat a lower note and then push it up using Melodyne.
 
I have one song that the entire harmony part is a simple raising of (generally) a third above the melody line - done using melodyne. I did this because I wanted to get it done quickly to see what it would sound like...and it actually did not turn out all that bad. Here it is if you want to listen: "Open-Eyed Girl".
 
Some things to remember if modifying the melody track into a harmony track:
>You will need to do a lot of fixing of formants and other aspects of the modified track.
>You should offset pitch and timing of the modified track.
>You need to know how to write a harmony line. As stated by other posters, it is not a simple matter of moving everything up a third, fifth or any given interval. It needs to fit withing the harmonic structure of the song.
>The bigger the change from the original note, the stranger the new note will sound.
>This works best on harmony parts intended to be in the background, not duet singing.

Honestly understanding what "reviewers" and "managers" and other laymen mean when they talk about your music is an art in itself. They'll say the vocals are off pitch and they mean they don't like the chord or they'll say it's too fast and they mean the arrangement is busy, etc.
Or they'll say "it needs backing vocals" and they mean your vocal sounded a bit weak (which could just be a level thing, or a mix thing) or that the choruses need another layer (organ, strings, whatever).

Unless you know this particular person and their background take their advice merely as "they didn't like it" and try to keep polishing your work as best you can. Get advice from fellow musicians you trust, check out tutorials about techniques and listen and compare to your favorite artists/songs. Putting lots and lots of time into backing vocals if you don't feel comfortable doing them, when you can't even be sure that that is why the guy rejected the songs, is a waste.

There's fantastic advice here. I'd only add that any effort you can put in to practicing nailing a harmony while the lead vocal is singing, then eventually learning to make up harmonies on the fly will pay off for you. There are tons of instruction videos on the net about this fascinating subject and one is out there somewhere that will work for you. It takes time but it can be done and is so worth the trouble.  It's just practice, right?

rbecker
I mostly follow what many posters have suggested...I write all the melody and harmony parts to midi tracks - one track per part - and then play the specific part I am recording voice for along when I sing. I record the main melody line first, then tweak it with Melodyne and otherwise get it in good shape, then mute the midi lead vocal, but play the sung lead vocal along with midi harmony_part_1 while I sing harmony_part_1...Then Melodyne and fix harmony_part_1 and mute midi harmony_part_1 and move onto harmony_part_2 etc.etc.etc...

This is worth repeating.
 
When you sing along to yourself you will get a much better interpretation of the flow within individual phrases which helps enormously when trying to keep the timing as tight as possible.
It's a real chore to have to fix the timing of words/syllables, especially on sibilant sounds like s's or t's - it sounds really amateurish to have the end of a word ending in s-s-s-s-s-s
 
Another way to overcome this particular problem is to only sing sibilant endings on your main vocal, don't sing them in the harmony overdubs, but watch you don't crack up with laughter when doing this!
 

I don't sing myself but I often arrange vocal harmonies for others to sing. If the vocalist is not good at harmonising against an existing lead vocal, I sometimes create a guide vocal for the harmony using a copy of the existing LV by pitch-shifting the notes using either V-Vocal or Melodyne. Although it always sound artificial, it's usually adequate as a guide vocal. It works better still if, instead of using the existing LV for this, I base it on a suitable alternative LV take (or clips from different takes). This way, although the harmony itself still sounds artificial, it will sound a bit more convincing alongside the LV.

Check out TC Helicon Voiceworks... 
 
This is a hardware vocal processing & harmony generator.. of which TC has made several versions.. Voiceworks, Voiceworks PLus, and the Voicelive Rack.. I own the first and recently purchased the latter...with my Voiceworks now going up for sale i suspect.
 
You can create up to 4 parts, each part derived from the lead vocal (which can be muted) but with each part having programmable male/female vocal shape (actually from troll/mouse), rise time, delay, vibrato amount, etc.. these can be fixed interval, set to scale, played in via midi note, extracted from chords charted or played (sounds very natural), and the latter version allows them to be extracted from chords derived from audio input. 
 
Given that early versions of the rack are ~$175 on Ebay this is a cheaper, simpler & quicker solution that mucking about with Melodyne once you have edited a couple of presets to your liking (and fwiw i do own Melodyne editor) ..
 
if you have more detailed questions thre are a ton of vids available and you can feel free to pm me.. 

Bristol_Jonesey
 
It's a real chore to have to fix the timing of words/syllables, especially on sibilant sounds like s's or t's - it sounds really amateurish to have the end of a word ending in s-s-s-s-s-s
 
Another way to overcome this particular problem is to only sing sibilant endings on your main vocal, don't sing them in the harmony overdubs, but watch you don't crack up with laughter when doing this!
 

Actually, I find myself sometimes doing THE EXACT OPPOSITE! If I have a tune where I feel the terminal consonant for a word was weak or missing....Usually a "t", "st" or "d" sound. I then create a special audio track in Sonar and sing along with the lead vocal, but ONLY sing the missing consonant! Played alone, this track sounds really strange, but when split up, mixed in and nudged back and forth with the lead vocal, can add some missing definition to the lyrics.

rbecker
...If I have a tune where I feel the terminal consonant for a word was weak or missing....Usually a "t", "st" or "d" sound. I then create a special audio track in Sonar and sing along with the lead vocal, but ONLY sing the missing consonant! Played alone, this track sounds really strange, but when split up, mixed in and nudged back and forth with the lead vocal, can add some missing definition to the lyrics.

 
Great tip! I'll be giving that a try soon.