Really, this comes down to any of the five major commercial broadcasters here (yes, even you, Nexstar). The Diamondbacks TV territory includes Arizona plus Las Vegas, Utah, and New Mexico.
Gray probably has the inside track simply based on coverage quality within Arizona. This is why they spent the big bucks to build KAZF and KAZS. They'd immediately also get Las Vegas. Salt Lake City is a bit of a question mark, as Gray is building a station there that will require multiple transmitters to correctly serve the Wasatch Front (the new KCBU, not to be confused with the old KCBU). And the company has no New Mexico presence, though Arizona's Family Sports is available on Fubo in the Albuquerque DMA.
Scripps is in a similar position. It does not have a Yuma station, but it does have stations in Phoenix, Tucson, Las Vegas, and Salt Lake. It actually owns duopolies in each market and has the secondary stations to air a slate of programming. Again, no New Mexico, but that's probably the least-important secondary market the Diamondbacks could serve.
Fox has to be considered, but the lack of any stations beyond Phoenix is probably what does them in. Fox has been less eager than other major broadcasters to add Big 4 pro sports and seems to only do so if it's being produced for them (KCOP has some hockey rights, and there are two notable WNBA exceptions, Seattle and New York). That would be the case in Phoenix, where KUTP is the GCU and ASU hockey station. But you're left with the same problem of signing up someone else to carry the ball in every other market, a someone that would have to be Gray or Scripps anyway at least for Tucson.
Tegna has the Phoenix and Tucson stations, but in Phoenix it lacks either a duopoly station or an easily identifiable secondary subchannel of KPNX. Local sports on a Tegna-owned NBC isn't unheard of. In fact, it's happened with the Indiana Fever (Tegna had the rights to 17 games last year, of which 7 aired on WTHR and 10 on WTHR's .2 subchannel and an associated Class A station). I think KING had some Kraken games on its own, too, this year. But you can't compare the Kraken or the Mavs, in Tegna duopoly markets, with the Diamondbacks.
Nexstar is a dark horse I would not have considered except that they just signed a deal for a Friday-only, 15-home-game package with the Texas Rangers. It's actually a historical shocker for KDAF in Dallas, which is airing local pro sports of note for the first time as a non-subscription TV station (read: over 40 years) and is probably one of the most underutilized TV stations in the country. Nexstar has the Vegas, Utah, and (unlike everyone else discussed) New Mexico stations, but again, Tucson would be a large issue, as would Yuma where options are particularly limited. They would also have to deal with a lot of people struggling with KAZT's metro Phoenix signal.
That brings us back to Gray and Scripps. Either one could do the job, but Gray probably has the edge because it can deliver Yuma. Nexstar or Scripps could still come in to fill the remaining markets in the TV territory, though beyond Vegas both are frankly gravy.