The Hogle Zoo had desert bighorn sheep and Chacoan peccaries in 2009, but didn't when I was last there in 2014. Are those species no longer in captivity?
Not sure about the desert bighorns, but regarding the Chacoan peccary, I know the Beardsley Zoo has a few. I'm confident they're not the only institution with them.
Both of these species are present in US zoos and have established breeding programs. Chacoan peccaries are held by around 20 facilities, while desert bighorn sheep are limited to a handful of institutions.