He prayed silently, ‘O God, give me any kind of death—without contrition, in a state of sin—only save this child.’
This priest is like Huckleberry Finn here, except that as a Catholic he can believe he will go merely to Purgatory, whereas Huck can only believe that he will go to hell.
Another importance difference: Huck believes he will go to hell for helping his friend, while this priest can no longer help his daughter, and he believes he may already be convicted for other sins that have nothing to do with his daughter.
Still, the priest does seem to be bargaining a little with God, offering that he'd be okay with dying at a particularly bad moment for his eternal soul (dying in a state of sin, as he says) if only God will look after his child. There's some common ground with Huck.