I've shot at 2 and hit and killed one in my life. I have a .243 which I beleive would be perfect for the job. Anybody know of a good place to go around Lea county or Eddy county where I might be able to make a day out of it?

If you ride the Carlsbad / Hobbs highway, you will see a bunch of road-killed yearling coyotes. Natural selection I guess.

Most people pick an oilfield road heading towards a remote oil pump and set up a calling station in the boonies. They are out there and there are a lot of them.

Trent, As Longrifle pointed out, the area between Hobbs and Carlsbad has a pretty high population of coyotes. I would suggest you take a trip to wally-world and purchase a DeLorme New Mexico Atlas & Gazetteer. This Atlas shows the county roads and forest/blm roads, it also has accurate color coded surface management. (don't want to be caught tresspassing accidentally). After you get your map you will see that there are literally thousands of square miles of public land in the area that you asked about, so any place that is colored green or tan on the map is a good place to start. The state land which is "lavender" on the map is a little more tricky. Some of it is open to hunting and some of it isn't , and it is up to you to know the difference. The closed parcels of state land are shown on another map that you can find on the NMDGF website in the section about "State Trust Land". Also in this section are the rules governing the public use of state land, very important to read and understand completely these rules before hunting on state land. And finally, private land which is white on the map. Unless you have signed written permission do not enter on to these lands.
Hope this helps, Ron.

Thanks, I saw a good sized one, shot on the side of the road today out at buckeye while we were checking out rabbits. Not cold enough yet. they still had flee's. Maybe late January