I can't recall fishing for carp in a standing water body. But I have caught some, accidentally, fishing in streams for other species. By using bobber & worms or worms OFF of the bottom. I've also gotten several while casting and retrieving surface plugs for smallies.
HOMEMADE BOILES for carp bait. Carp eat both plant matter and meat. The biggest movement in carp bait is a homemade doughball combined with fish scent and color then boiled to firm it up to help it stay on the hook. Lots of recipes include berry flavored jello. Lots of videos out there on the subject and creative ideas on what to put in them. Some additives I've been wanting to put in the blender to try out in boiles but haven't gotten around to yet are clams, crawdads and goose poop.
If you go on Youtube, there is a channel called Bait Vault. You can find all kinds of boilies, packbaits, hookbaits, etc...
I've made their recipes and have created some of my own, as we go out for carp often. They work.
We used to get huge carp off canned sweet corn as well! I will never forget the day my friend was in charge of bringing the corn and behold.. a fresh can of creamed corn.