There are a couple things that I can think of in this story that are ironic.
First, it seems somewhat ironic that a boy who is supposed to be fated to die soon would want to withdraw from the world. It seems more as if someone like that would want to embrace life.
Second -- and this is the one that I think is a much better example of irony -- is that Conradin's faith is justified just at the moment that he loses it. When he sees "the Woman" go into the shed, he knows that he does not believe that his god will grant his wish. But right at this point where his faith is lowest, his greatest wish is granted. This is ironic because you would expect that a person's faith would be repaid when he has the most faith, not the least.
At first, It is ironic that in the beginning of the story it was set that Conradin is going to die in five years but instead of Conradin, Mrs. De Ropp died.
Another thing is, his worship to the god Ferret which he thinks that will answer his prayers he started from the little faith and fulfilled his most precious desire.