Your best bet for hunting Merriams, and the nearest from Clovis, is going to be the Lincoln National Forest. There are birds scattered throughout the Ruidoso/Capitan areas where there is water and roosting habitat, but there are also large areas where there are no birds because there is no surface water available to them. The area around Cloudcroft/Mayhill has more birds, better habitat, and more reliable water sources throughout the forest.
Also, there are opportunities for hunting Rios on the east side of the state, as well, and I would guess there are places closer to Clovis where you could hunt those instead. Unfortunately, I am not as familiar with the Rio hunting opportunities over your way. For pure Merriams birds though, I would go to the Cloudcroft area.