Checkout the North Platte Fly Shop web site, they do guided Carp trips and provide some pretty good information on Carp fishing.
Local Carp Fly Fishing Reports
The chart says there is carp in Golden Eye Reservoir, it is 6.5 miles past Natrona on hwy 20/26, roughly 36 miles west of Casper.
Here is some pretty good information on how to catch carp on a fly rod:
How To Catch Carp On The Fly
What days will you be in Casper? I have never fished for carp but have been interested in doing it sometime. If your interested, maybe we could fish together. Are you knowledgeable enough about carp fishing where we could use my boat or maybe we could check with the North Platte Fly Shop and split a guided trip if they have a day open.