Okay, sorry for sounding like a wuss, but I mainly fish for Bass and Sunfish, but one small lake I go to is loaded with Carp. I use ultralight gear, so just hauling them onto the bank isn't an option. Do you 'lip' them as you would a Bass? I guess they don't have teeth, just their mouths kinda give me the creeps. Thank's.
Most of us use a net. You can buy a long-handled Ranger-brand net with a deep, soft mesh bag at Academy for about $15. I have also used a cheap trout net with a deep bag that easily handled a 10-pound carp, so that might be an option.
Without a net, you can try to tire them out until you can lift them out of the water by putting your hand(s) under the belly, but in hot weather that can affect their ability to recuperate in poorly oxygenated water.