Can any other saiyan attain Super Saiyan Rage?
Trunks's first actual super saiyan transformation was when he saw his role model Gohan die after that he got really angry and swore revenge on the androids. 

A reason Goku cant get super saiyan rage is even though he got mad and transformed into a super saiyan and wanted to avenge Krillin he wasn't as mad as Trunks as you could see Trunks got so mad that his tears were being vaporised off his face. 

A reason it didn't happen for Vegeta was that he was super Vegeta, a custom super saiyan based more on ki based attacks and super Vegeta can only transform twice so he still wasn't as mad as Trunks.