As Gustavo pointed out, Nine Volt Audio has a great set of samples called Shimmer and Shake or something. Fantastic percussion samples including tambourines.

I got it for a great price nice they are going out of business. Probably even less cost now.

Really great for what you are asking to do.

EZdrummer Latin Percussion has awesome tambourine sounds and Midi patterns.

 When I was working on this tune, I scanned all of my libraries to find a shaken tambourine, to no avail.
The tambourine here is from DimPro. I softened the attack(ADSR) to kill off the initial thwack.
From there, I used my controller to manipulate velocity.
May not be quite what you are looking for, but might give you some ideas.
http://soundclick.com/share.cfm?id=10285834

A crappy tamb played well will sound better than great samples not programmed right. Just grab one and do it yourself. The tambourine is harder to play than people think, but it is a very rhythmic one, you'll find a cool pattern way faster by just shaking one.

I did a synthetic tambourine part for an acoustic "bonus version" of a song ("My Lucky Day," written by Mark Longworth). Normally I would use an acoustic tambourine, but didn't have one handy. The part used a single sample from the Fantom VS, but it sounds very realistic because of the velocity editing. If you want to hear what velocity editing can do, go to https://www.youtube.com/watch?v=2tvt6DluvoA and you'll hear it kick in at around 45 seconds.

dlesaux
EZdrummer Latin Percussion has awesome tambourine sounds and Midi patterns.

I agree, and much more as well.

The occasional off beat hit? In my experience Tambourine players sometimes lose focus on the tambourine during the song and push and pull on the timing in a way that is more than swing. dropping a beat in a measure or adding one. Not all the time, but sometimes.
 
And I'm not trying to say that it's just bad musicians who play tambourine. It's often singers who have a lot of other things to think about.
 
The other thing I find is with acoustic groups that tend to pull out tambourines, the tambourine goes into lots of microphones on the stage sometimes causing interesting phasing fx. So for this reason, copying the track and nudging it a few milliseconds, then using a ctrl+drag sign line at a very low volume and panning left and right might be interesting.

I understand the OP and what I have done is sample my tambourines with shakes and hits and make sure each sample has only 1 movement of sound (LEFT then RIGHT)... I then can sequence shakes and hits very realistically.  The key is to get the samples right (and many of them, with multi velocity layers) to avoid the machine gun sound.
 
It is also good to sample the tambourines with only a ROOM or OVERHEAD mic to avoid the harshness of the initial transient attacks and it gives the tamb some AIR feel to it.  What ever you do, don't sample the tambourine (or record a track) with a close mic only.... if you have ever done this, you know what I mean.
 
Jim

...wicked
A crappy tamb played well will sound better than great samples not programmed right. Just grab one and do it yourself. The tambourine is harder to play than people think, but it is a very rhythmic one, you'll find a cool pattern way faster by just shaking one.

I swear this was exactly what I was going to type to you. fooman. Wicked is spot on...honest, you'll mess with samples longer than you will if you recorded the tamb with even a kids tamb and a Radio Shack mic. I definitely recommend recording a real one and just experimenting with your mic placement so that you get the whole sound of the tamb without mic'ing too close. I just did one the other day using two mics that sounded great and the tamb the guy had was nothing to brag about. The ones I have at the studio were 100% better but he wanted the one he brought. It wound up sounding great. So if you can borrow one, definitely try doing it yourself. Like Wicked, I'll take a bad sounding tamb over the sampled ones. :) Good luck.
 
-Danny

I often do play the parts.  Or have the client do it if it's during tracking.
However, not all percussion instruments are made equal and sometimes I'd like a tighter sound, different timbre of instrument, etc.  So I'd just like to get some midi going for this reason/situation.

I bought the Shimmer and Shake package.  Was only $30 or so.  However, I found that my lack of knowledge with how REX loops work is killing me haha.  I found that the loops are often a lot faster once imported/dragged into the session, compared to the speed they play at when previewed.