To me, since the show was essentially a wild west shootout in the future, having the rapid fire run n' gunning is just nope.
Sunset Riders is basically just Metal Slug in Dodge City. It's kind of dumb, as a result.
The list of games I can think of that have a cooler shootout feel to them are....
Golgo 13 and Mafat Conspiracy
Rolling Thunder
City Hunter
Codename Viper
Shinobi
Cyber Cross
The idea of a Gunsmoke style was tempting for about 30 seconds.
PCE has enough shmups.