# Peculiar MCMC sampling problem

I have two random variables, X and Y, and Y is a positive real number. I can sample from $$p(y|x)$$, but I need to sample from $$p(x)$$, which I know to be proportional to $$\frac 1 {E[y|x]}$$. I could estimate $$p(x)$$ from the mean of a lot of samples from $$p(y|x)$$ and then use a Metropolis algorithm, but sampling from y isn't cheap, so sampling a lot of them for each step is somewhere between prohibitively expensive and ain't gonna happen. Is there a better way to do this?