I know there are a few used parts places around Belize City and a couple elsewhere.
Keep in mind that Belize's entire population country wide is only about 265,000, and that only a small percentage, less than 10%, own cars. So while there's surely demand for used parts, and plenty of bad roads and bad drivers to create junk cars, the total market is quite small.
Before you get too far along in your plans, you should spend some time in Belize and see what the situation is.
--Lan Sluder