I have an audio CD to mail and have already printed the label via PBS.  The member is now requesting that I mail it to someone else since he is giving it as a gift.  Am I allowed to rewrite the label?  I assume not, but wanted to check first. 

If you bought postage, I don't think you can.  If you just printed the label without postage, yes, you can re-write it.

You can reprint the original label.  I'm not aware of any options for changing or rewriting a label without loosing your postage.

He messaged me a link for creating a custom label, but it says I have to rebuy postage.  And I don't trust rewriting the label, because then if the package gets lost, I would think I would have no recourse.

Yea, if you bought postage, I don't think you can change the address.  You MIGHT be able to take it to the post office and have them change it.   There is a place in the requesting process where you can confirm your address or click to mail to a different address. He should have done it at that time, not after you've already printed the label.  His fault, not your's. I'd mail it with the postage-paid label you've already printed and let him send it on to the other address.  

If you printed postage you CANNOT change the label in any manner. The information is imbedded in the endicium on the label and if it gets looked at and the address on the label doesn't match whats in the postage, it will either come back or arrive postage due. I would tell him it is too late to change the address or they will need to pay for the additional postage. 

I would suggest to him that you he can either receive the package at the label that you already printed; OR if he wants to save time, you could use the new address if he sends you a credit to compensate for the old postage label that you can't use.