Emus and Rheas. Although Rheas are rather aggressive and violent, even potentially when raised as a chick to an adult by humans. Otherwise, mating with any bird smaller than an emu will likely just cause them pain, and for birds around the size of a chicken may even cause death to the poor critter due to internal trauma.
Ostriches and Emus are sort of like mares in the sense that if they do not want you sticking your dick in them they are more than capable of defending themselves. Often with deadly results.