I like bugger type flies for when they are rooting around. usually try to come up behind them and high stick. Tie them with lead eyes or beadchain to ride hook up. Dragon fly nymphs like RLDs work well also.
If they are cruising, I would rather throw a white bugger or similiar white minnow imitation. You want something to slow sink evenly, not so heavy it head dives to the bottom.
If they are skimming the surface, a foam beetle can be productive. Watch directions of movement and place it in their path just like a rising trout.
Carp can be very technical and other times very easy. They are sure a lot of fun.