A lot depends on the age of the bird - if it's under 12 weeks or so (like most CornishX), a couple days is good. The older the bird, the longer you want it to go, up to 4-5 days (I did a year+old rooster for 5 days a bit ago).
Resting is to be done in the fridge, but it can be done before or after freezing. Freezing stops all the chemical/muscle processes that are important during resting. If you don't have the space to rest them in the fridge after processing, you can freeze right away. Just take the one out you want to eat, thaw it, and then let it sit in the fridge for the right amount of time that it should rest - 2-5 days depending on it's age.