As a private seller, if I sell a handgun to someone who bought another handgun less than 30 days ago (knowingly or unknowingly), can I get in trouble? Or is it completely on the purchaser, in a private sale, to make sure they abide by the 30 day rule?

You have no way of knowing.  So as long as it cannot be proven you knew at the time of sale, you are ok!  Buyer's butt is on the line when you mail in the P2P copies to issuing department and NJSP with the date on it.

All on the purchaser.

On the buyer since he is the only person who would really know.  

As a private seller, am I even obligated to ask the buyer if they purchased a handgun in the last 30 days?

No

It's on the buyer, if he/she is honest and says he/she purchased one already within the 30 day period without the exemption paperwork (and had copies to backup his/her claim) I would refuse to sell it. If the buyer lies and ends up getting caught it's on them not you.

The only way you (the seller) could have a problem is if you sold the same buyer more than one handgun inside 30 days.