How do I modify data to test retest measure as more normal?

Pearson's $r$, as well as other correlation coefficients, are popular choices for assessing retest reliability, but they aren't very good ones. The problem is that correlation coefficients, by design, adjust for differences between the variables such as additive bias and rescaling. When you're looking at retest reliability, on the other hand, you want to check to what extent the test gives the same scores between administrations, as opposed to merely correlated scores. So you're best off with something like root mean squared error or mean absolute error. Having data that isn't normally distributed, by the way, isn't an issue for either of these.