Get you a burlap bag and put in a few pounds of dry dog food. The cheap stuff actually has a better scent for drawing them in. Now, with you in Texas, get yourself a good Jack Rabbit in distress mouth call. set off about 30-50 yards down wind of the dog food bait. Hit that distress call for a few seconds with an up and down cadence. Keep your eyes peeled. After about 2 minutes, hit it again. I usually do that 3 or 4 times then hang around that spot for about 1 hour while hitting the call every few minutes. If no responses within an hour, you don't have a yote in hearing range. If you do see one sneaking in, and it heads to your bait bag, give it a couple minutes because more than likely he has a buddy or 2 with him. They will all eventually come in to the bag and start fighting over it and it doesn't take long for them all to get in. They usually "send in" the idiot youngins to check out the bags. Once you feel all of them are in on the bag, let loose!

As to the OP's question, I've dropped many yotes with a 22mag out to 100 yards. Done it with solids, hollow point both and they both put them down. Pretty much whatever cartridge/bullet shoots the best from your rifle will work. It's not my PREFERRED cartridge to use on them as my .220swift or my .22-250 gets the nod for that work but I've cracked more than a few out the back door when my .22mag was sitting there and not one of my loud babies :D

But a 30-06 can make some nice coyote holes
 

Some folks hunting deer get to wedge a coyote.

And you get to see one if you're not on an iphone all the time.

I've killed coyotes while squirrel hunting using 22lr subsonic HP's. They run but they die.