Although there are scenes that make it clear that it's a 29 in Season 2, I believe he was carrying a Model 19 in Season 1.
This picture in particular looks like a 19 to me... more barrel in front of the ejector shroud than a 29, and smaller cylinder:
There are a couple of scenes in season 2 where the M29 obviously a new production 29, not a period correct model.
There's also a scene where Jim Chee's mother has a 4" Python, that appears to be a new production stainless Python.
I've long been a fan of Hillerman's novels, and these adaptations take a LOT of liberty with the characters. At least the technical advisors are trying with the firearms to be period correct. Nobody but us gun nuts would probably notice the inconsistencies!