I'm starting to plan for the engine swap I need to do for my Jeep and I have a couple questions about registration and emissions testing, especially seeing I plan to swap a small diesel into it.

What paperwork would I need to do to amend the registration and what would the emissions testing issues be ?

Never heard of anyone needing to do anything. Lots of hot rods running around.

What year is the Jeep? No emission testing for 1974 & earlier. 75 and later, you go through DEQ if in the tri-county area.

It's a 2008 and it has to remain street legal as it is my daily driver

30 years ago I had a 78 VW transporter, the engine blew so I had an earlier model swapped in. I don't remember the year, but the first time I went through DEQ the guy told me I didn't have a catalytic converter.  I let him know that the engine didn't have one because it was a 1972(maybe) engine.  He said it didn't matter since the van was newer and required one.  So make sure the motor would pass DEQ, if not register it outside Metro or get a trip permit forever.  
No paperwork was required because of the new motor, but it did still have to pass DEQ for the year of the vehicle.  Good luck!