I am not an expert in this area but here are a few ideas you can play with. I am sure you will get some good answers from other people.

1. You can calculate Pearson correlation p-value. Almost all the statistical packages can do that.
2. You can also try permutation based testing to assign p-value. Basically you permute your data several times and then compare those correlations with your original one. If those correlations are as good as the original calculation then the original correlation is week or merely a noise.
3. You can do some meta analysis where you can combine information from literature about genes that are known to be correlated in your tissue of interest. For example, you can select genes from a known pathway and check how good their correlation is in your data and then come up with a score.