Is there a way to mark a sender that I do not want to receive from?  So then if I would be getting a book from them, they just won't offer it to me? 

No.

PBS is not set up to screen transactions in this manner.  Luckily membership is large enough that you are unlikely to be matched up again FIFO.  If the person is posting directly to your Wishlist you could  increase your privacy settings so only friends or nobody can see your wishlist.  If the other member is already a friend, you can unfriend them.

I just keep a list of members with whom I've had negative contact.  The list is very short so easy to glance at quickly before completing a request. (after sender "accepts" your book order, you can click on PM and see who the sender is, then just click out of it without sending a PM)

Jeanne's suggestions is not quite accurate. I think what she means is that immediately after requesting a book, go to your My Account page and check your list of "Books I've Requested". This should be done before the sender even sees the request or accepts it, not after the sender accepts. You can then click on the PM button to the right of the book title to see who the potential sender is. If the sender is someone you don't want to trade with, you can click your browser's Back button without sending a PM, and then click on the Cancel Order button to remove it. 

Normally, a sender shouldn't see a request for an hour after placing an order, so you do have a little time to check before deciding whether to go ahead with the order or cancel it. This is sometimes referred to as "requestor's remorse". If you cancel an order shortly after requesting it, the sender shouldn't get an email from PBS that the book was requested and won't know anything about it.

You can then click on the PM button to the right of the book title to see who the potential sender is. If the sender is someone you don't want to trade with, you can click your browser's Back button without sending a PM, and if the sender is someone you don't want to order from, click on the Cancel Order button to remove it.

Yup, and then keep checking on it some more until it gets accepted, because if the first potential sender denies it for some reason, the order will roll over to someone else and you won't even know unless you are a very noticing sort of person.