I've seen a few sources over the years that say Perry's original drum machine, and the one used on Marley's "Natty Dread", was a Gibson Mestro Rythm King. It was a box that was very similar in concept, sound and function to the "percussion" sections that were often part of the "home electronic organs" that were popular in the 70s. They had a few pre-set fixed drum partterns, called things like "waltz", "polka", "latin" etc.
There's a youtube demo of a Gibson unit here -
https://m.youtube.com/watch?v=u7b1KMc7xosMost of these sounds are actually pretty easy to synthesise or replicate by abusing modern drum and electronic drum samples - severe bit reduction can usefully work the opposite of hi-fi, add in some eq and transient shaping. And remember that there are no accents and the pattern is fixed unless you e.g. remove hats and cymbals using a steep low pass filter (or a steep hi pass to remove the kick). Or isolate a single beat and pass it through a grungy delay and create patterns that way.