What size drill bit do I need for a 3/16" plastic anchor in tile?
If you are wary of making the holes larger (which is possible and as Tester101 says just make the hole in the tile larger) then you could just go for a smaller anchor and screw.

Obviously this will depend on whether the smaller screws are still a good fit for the holes in the hook. Also the load the hook can take might be reduced, but as you're not going to be swinging from it (hopefully!) you should be OK.