Does anyone know of a company on St. Thomas that rents baby car seats? The car rental place at the airport does not have any available when we arrive. Thanks!

I really recommend bringing your own. You can check it with your luggage or gate-check it (or bring it on the plane if your baby has a seat).
The car rental companies can not help you install it, it may be old, damaged, dirty, or not available even if you reserved it. Plus you pay an extra $10/day or so for it.

I would absolutely bring my own. From experience, pb and j is absolutely right. Four times in a row, we got the same nasty car seat. After a while, we could recognize stains from the year before. Yuck. We finally bought a carseat/stroller from "TriplePlay" and it was a wonderful investment. Very well made, comfortable seat and so convenient to have the stroller all in one. I don't know how we survived without it. It may seem like a hassle, but you'll appreciate having your own and not subjecting your precious to any old seat.

Thanks to you both. We've decided to bring our own car seat. Fingers crossed that everything goes smoothly.