Temple Gun Club along with ARC run monthly matches. I think they both do High Power, and Service Rifle. ARC also does Silouette. Place called Rifles Only down by Kingsville also does training and ran a few sniper comps. As mentioned Tiger Valley also has a good schedule. Not sure about IDPA like orgs for rifles, but you can look into a 3 gun organization.

ETA: You can also check the Texas State Rifle Association web page and see what they have up.