Keep it simple. #6 or #4 hook, some sweet corn or a crawler gob, split shot for weight. Slip sinker rigs work well, too. There is a ton of info on the good ol’ interweb, as the Brits have been finesse rigging carp for years. Those guys sure know how to make a relatively simple thing pretty darn complicated.
If you watch the carp long enough, you’ll see that they often follow the same path back and forth through an area, like deer using trails. Cast your bait into that trail. When they’re close to shore, you can sometimes see them take the bait. That’s a lot of fun.
Things might be a little slow right now, depending on where they’re at with the spawn. They aren’t too interested in eating when they’re doin’ the nasty.
Good luck!