can they?

Question
can two different parrots(lets say an african grey and a double yellow headed amazon) have babies?

Answer
I doubt in your example it would work and it certainly would not be a healthy practice and the babie would likly have all sorts of genetic problems. Now if they are close enough related such as a jenday conure and a sun then they can have babies called sunday conures. Breeding hybrids is always discouraged because it taints the blood lines of the pure birds.