Wikipedia shows a 41% increase in population in the 1970s - why was that and can that be maintained over the next few decades?
Here's a less plausible but possible one: Bowden Wyatt doesn't leave Wyoming for Arkanss after 1952, and thus he doesn't get to have the offer when he did for his alma mater of Tennessee after 1954; or he sees something with segregation that disgusts him and he decides to go back, figuring that he won't have to deal with it in a state where there aren't many blacks anyway. Or,if he was secretly pro-integration, he starts luring blacks to Wyoming. The man is a Hall of Fame coach and led Wyoming to an undefeated season and Gator Bowl, where they finished 12th in the Associated Press rankings.
Maybe an even better option would be Tennessee doesn't open up and he goes back to yoming, but either way, he also avoids an earlhy death by some years and lives to coach the team into the '70s where someone else relly good comes along. The gist is this:
Wyoming changed conferences in 1962. But, TTL a big argument ensues and somehow a few teams from the former conference Wyoming is in don't get selected Denver keeps its program instead in the new WAC. The Big 8 has been established for years - Bob Devaney is about to come from somewhere else and really revive the Nebraska program since he wasn't at Wyoming - and Wyoming decides instead to petition to join the conffrence which would one day be the Pac-10, but which was just then adding Washington State. Their success led them to be considered, but for now, they joined with Oregon, Oregon State, and Arizona and Arizona State with 1-2 others in their own conference. Eventually, they join the other 4 in the Pac-12 by 1978, as Utah, BYU, or Utah State are also invited to join.
The success of the program - even if middling till it starts playing the Pacific coast teams more frequently and getting better and better players - lets the university become nationally known. It becomes, if not a powerhouse program, like an Auburn, one which will have a few really good years, potentially a Heisman winner, etc.
So, more and more people start coing to the university who are major players in new industries - including computer science. Wyoming doesn't become TTL's Silicon Valley, but it does become where some smaller startups ave their headquarters because it's near their alma mater. Cheyenne, as the seat of government, becomes a more vibrant city, too, being so close to Laramie and the University of Wyoming.
Then, the miracle happens. In 1988, the team beats West Virginia in a nonconference game and wins all their others games, but one loss keeps them out of the Rose Bowl. However, they do so well they are number 2 in the nation, with only one undefeated team - Notre Dame. Wyoming was in the Rose Bowl the year before and lost, and now, they are playing NOtre Dame in the Fiesta Bowl for the "mythical national championship."
They lose. But, after 2 straight years of national prominence, even more people start flocking to the Unviersithy of Wyoming as so much free publicity is given about all they offer. That gets even more people to attend - and, more importantly, the right ones as society is changing and they have the companies to facilitate that.
It's not much - it certainly can't make Wyoming a top ten state. But, the number of computer and other companies as the world becomes more of a computer-based ones means that Wyoming has doubled their population from OTL and now has over a million people, with a... well, maybe not a megalopolis by any means, but a large developed area around Laramie and Cheyenne that is just good enough to dream.