Not elegant, but it worked for us on our old boat...
1) put a couple of screws on top of the fiddles, leaving the screw heads sticking out about 1/4 inch.
2) figure out where the table lies on top of the screw holes
3) Drill small holes the size of the screw heads in the bottom of the table (but not through it!) where the screws go.
4) Now, when the table is down, the screw heads should be inside of the table, preventing it from sliding off the fiddles.