As background, Colorado's process for nominating Presidential candidates has been quite fluid in recent history. Often, there is a Presidential primary months before partisan primaries for other offices (affording a second chance to vote that isn't very disruptive if necessary). Some years, Colorado has had a caucus rather than a primary for the Presidential race, and the two major political parties don't always nominate their Presidential candidates in the same way or at the same time.
Lots of things could happen. If the U.S. Supreme Court stayed the Colorado Supreme Court ruling pending its consideration of the case on the merits, another Colorado court could put the Colorado Republican primary on hold until SCOTUS decides it. Or, the state legislature might pass a bill postponing or dispensing entirely with one or both Presidential primaries.
If this didn't happen and the primary election was held, the results might be invalidated and the nomination from the state might be left to the caucus process or the party leadership, the state's Republican party might send uncommitted delegates to the national convention, the resolution could be moot if someone else won the GOP primary in Colorado, or the runner up in Colorado might get the state's GOP delegates to the national convention.
The exact wording and language of a SCOTUS stay and of a status ruling, state court actions, internal Colorado Republican Party actions, and national Republican Party actions (particular the actions of the credentials committee) could all matter. Colorado law can regulate how the Colorado Republican Party nominates its delegates to the national Republican Convention where the Republican party chooses its delegates, but can't control whether the national Republican Convention will accept those delegates as valid.
This would be a basically unprecedented situation. The law is quite prescriptive about how the process is supposed to work. But when some unavoidable external circumstance throws a wrench in the works, the relevant actors in the process have considerable leeway to fashion remedies in that situation.