Republic of the Rio Grande is a no go. It was basically a paper republic. Advocates for creating a republic did meet in Laredo in 1840 concerning the creation of a republic, and they did manage to form a government and arm some volunteers, but the actual state governments of Tamaulipas, Nuevo Leon and Coahuila never got together to actually make it a reality. There just wasn't any real support for it.
That said, one idea I have is based on a thread someone posted here a few years ago. Maybe you can have the Spanish pursue more aggressively the colonization of California (earlier discovery of San Francisco Bay, early discovery of gold, whatever...) and sometime in the 18th century a much more populous California becomes a separate Viceroyalty from New Spain. When Spanish America clamors for independence later on, you end up with a Hispanic republic encompassing more or less the territory in the OP. I don't think it'd be called the Republic of Northern Mexico in this case, but if you fancy that name more go for it.