A DSLR maybe? The Canon XT has a cycle time of 0.4 sec
I think the best compacts have at best 1-1.2 sec cycle time
Actually the Fuji S5200/5600 has a cycle time of 0.7 sec for 3 shots and then slows down to 1.2. Not a compact camera though, but a fairly compact ultrazoom (10x) with decent high ISO performance (iso400) and competitive pricing.
What camera do you have now?