Do your new coils have diodes on their lugs I'll take your word for now (for science) that it literally came with capacitors and not diodes - so this is a separate thing, but make sure your coils have diodes pre-installed across the lugs. I think if they didn't it may just do it immediately though, so that MAY be ruled out. If you replace the fuse and play a few more games, will it blow again? The thing with fuses is that sometimes they're a little old and you may find their tolerance to be a bit wacky - meaning sometimes if you blow a fuse and replace it it won't blow again. And if it does, it's very cheap to just throw another in assuming you have a few on hand or near you in a store...

Somebody else may be better off chiming in on the capacitors, I'm honestly not quite sure on that. All I can recall about capacitors under the playfield in solid-state machines is that they were used on old Ballys to make the playfield switches more responsive - I don't think I've ever seen them used on flipper coils. Makes me wonder if it's for the end-of-stroke switches? I don't think it would be for the coils themselves, that would be strange.

(QUICK EDIT: I was also thinking cabinet switches as a possibility, but I just read ForceFlow's first response, there ya go! )