Catcher hasn't been a position of strength throughout most of franchise history. Certainly we've had solid players playing the position, and a few All Star selections as well (Miguel Montero twice, Damian Miller once.) Both of those players make that list, interestingly both for seasons where they didn't make the All Star team. Candidates are listed in alphabetical order, by last name.
Welington Castillo, 2015
Castillo didn't even take a full season to make it on to this list, but although he does have the fewest plate appearances of anyone (303), that's only 15 fewer than Kelly Stinnett had in 1998. As for how he performed? I won't go into great detail, because it's fresh in our minds, but 1.4 bWAR, 1.7 fWAR, 17 home runs, an OPS+ of 116, and positive defensive value by UZR. Given what we expected from the position entering the year, this was beyond successful.
Damian Miller, 2000
While Miller had a number of solid seasons in the desert, and was selected by Brenly to the All Star team in 2002 (and likely would have been MVP had the NL won), it was his 2000 season that was his finest. This, despite appearing in only 100 games. But this was the peak of his defense, which would decline in subsequent years. He also wasn't poor offensively; although he came to the Diamondbacks with the expectation of being a defensive catcher, his bat was a very good asset. 2000 saw him post career high marks (minimum 200 plate appearances) in OPS+, batting average, and on-base percentage. His defense also rated at career-high levels by advanced metrics (which weren't quite as advanced in those days, but whatever.)
Miguel Montero, 2012
Miggy's best season (and the best by any Diamondbacks catcher by fWAR) was in 2012. Yet, like Damian Miller, he didn't make the All Star team that year. But how good was he? He played in the most games and had the most plate appearances by any catcher in franchise history, and he was good throughout. Fangraphs rates his defense in 2012 as second only to Miller's defense in 2000 in club history (minimum 200 plate appearances). He posted the highest wRC by a catcher in franchise history (125) while posting a career high in OPS+. Oh, and he also finished sixth in the National League in on-base percentage, at .391. For comparison purposes, his batting line in 2012 was almost identical to that of Paul Goldschmidt. Montero was worth 4.7 fWAR and 4.1 bWAR.
Chris Snyder, 2008
Snyder isn't remembered that fondly among Diamondbacks catchers, but his 2008 season would have been interesting had people talked more about the three true outcomes in those days. His .237 batting average doesn't look particularly good, but his 16 home runs and 13.9% walk rate (along with a 25% strikeout rate, of course) helped him to an OPS+ of 103. In D-backs history, there have been three seasons by a catcher (minimum 200 plate appearances) with a walk rate of 13% or higher. Chris Snyder owns all of them. On the other hand he also owns 2 out of 4 seasons with a strikeout rate of 25% or higher. In 2008, Snyder had one of the three true outcomes in 42.8% of his plate appearances. He was serviceable defensively, and posted 2 fWAR and 1.8 bWAR.
Kelly Stinnett, 1998
Unfortunately, Stinnett wasn't the first person behind the plate in franchise history, that honor going to Jorge Fabregas. But he did play the bulk of the inaugural season behind the plate, with 92 games and 318 plate appearances. Even in that limited time, he was able to put together the fifth best season ever at the position by fWAR, racking up 2.1 fWAR. (Of the four better seasons, two are on the list above, and the other two were also Miguel Montero.) B-ref didn't like him as much, giving him 1.6 bWAR. But he was a bright spot on a team that wasn't very good. He outperformed Travis Lee (he of the sky-high expectations) despite having about half of the plate appearances. Of course, this was pre-Moneyball, and a catcher who posted a .353 OBP just wasn't as in-demand as he would be now. But his 107 OPS+ and solid defense clearly proved valuable; the D-backs went 34-45 when Stinnett started behind the plate, and 32-51 with other catchers getting the start.
Vote below for the starting Diamondback All-Star catcher, or write-in another candidate.