The term "double action" comes from the type of trigger that allows the gun to be cocked and fired with one motion - two actions, hence a "double" action, as opposed to a "single action" where pulling the trigger performs only one action, firing the gun, with the cocking being done separately.
So a DA rifle would not have to have a hammer, only a trigger that would both cock and release the firing mechanism. I can envision such a thing, but for several reasons the mainspring (firing pin spring) of a rifle is usually much stiffer than that of a revolver and beyond the strength of most trigger fingers. (Think retracting the firing pin on a Mauser 98 using only the index finger.)
So it is a lot better to cock a rifle's firing pin by the same mechanism (manual or automatic) that is used to load the rifle rather than using the trigger.
That being said, I know of no double action rifles or shotguns (other than those adapted from DA revolvers).