wood slat table

[South Jersey Styx]

Are you saying that the table is made of wood boards/slats nailed closely together and there are spaces between each one?
If so, caulking won't help. Without some time of backing or support, the caulk would "slip" through. Plus it would not look very nice.

I agree with kadyady and just get a decorative tray. There are a variety of styles including wood or silver/metal. Alot of people who use ottomans as coffee tables use this idea. Good luck with your project!