I lived in Maverick County for 5 years and enjoyed the hunting. If you will have a host/guide who's from the area, he should be able to fill you in on the best methods for yotes and bobcats. Find out whether you can take a cougar, too, since they range in parts of that county. Doorunner & GS both were right on the money with their advice.
A couple of other pieces of advice if I may:
1. If you decide to go to Mexico to "see the sights", make certain there is nothing resembling a firearm or ammunition on your person or in your vehicle. The vacation could end up being a lot longer and less pleasant than you anticpated. Your rights as an American citizen cease to exist when you cross the "Rio Bravo".
2. If the weather has started to warm up, be aware that there are some big rattlesnakes out there. No need to be paranoid, just use good sense.
If you have never been to the South Texas brush country before, you are likely to find it quite an adventure. Let us know how your planning is going. Hope you have a great time. Bust a critter or two for me.