Here is a link to Mr. Hirsch's website:
Texas Gun Trade: Sporting Rifles
I don't find anything to answer the question regarding long arms for the early Texas Rangers, but there is a lot of information there about the guns that were available on the early Texas frontier. If we can find transcripts of the actual papers issued by Stephen Austin for formation of the ranging companies, he might have specified how they were to be armed.
I think in that early, 1821-1830 period that was mentioned, the rangers and frontiersmen would have most likely been carrying flintlocks. Here is a quote from Noah Smithwick's
Evolution of a State, concerning arms carried during the Texas Revolution of 1835-1836:
"...
long, single-barreled muzzle-loading flintlock rifles..." This .51 caliber rifle, marked
G. ERICHSON HOUSTON, TEXAS may be similar to what Smithwick was describing:
Interestingly, it is a half-stocked flinter. Questions come up now and then about these, and whether or not they existed. This one is thought to have been restocked, which has been described in several period accounts of life on the frontier, but it was not converted to percussion. These half-stocked flintlocks might not have been common, but they surely existed.
The next one shown is a .50 caliber plains rifle made by Jacob Linn of San Antonio. One is actually dated 1851, so it is of a style later than the 1821-1830 period, but it looks like the type carried by the fellows in the image.
The .56 caliber Texas-made rifle below is marked
E. KRAUSKOPF A FRIEDRICHSBERG. Based on accounts I have read of the western frontier, rifles of around 40 [0.488"] to 60 [0.427"] balls to the pound were considered adequate for big game. This .56 caliber rifle would have used balls of around 28 to the pound, or 0.550", I'm guessing. The early Texans liked big bores! I think this was probably not just for hunting, but for fighting. In those days, when everybody was mounted, guns had to be big enough to take out a horse. If you kill the horse, which is a bigger target, you have effectively taken out its rider. It sounds brutal, and it was, but that was the reality of life on the frontier. I believe the early Texas Rangers were actually employed more as Indian fighters than law enforcement officers, and the Comanches with whom they did battle were famous horsemen. I will say most of this is "informed speculation" on my part. I'm not saying any of the guns above actually did service in the hands of early Texas Rangers, but I believe they could have.
Note the scrolled triggerguard. The Hawken brothers were not the only ones to use this, and Mr. Hirsch shows several rifles with Texas affiliations that have this feature.
I know we have a few Texans on this board, ardent students of Texas history. I hope they will contribute to the discussion, maybe add some thoughts and correct my errors.
Best regards,
Notchy Bob