What regulations surround fitting aftermarket fuel tanks inside the cabin?
This is covered by 14 CFR 91.203:


  §91.203   Civil aircraft: Certifications required.
  
  ...
  
  (c) No person may operate an aircraft with a fuel tank installed
  within the passenger compartment or a baggage compartment unless the
  installation was accomplished pursuant to part 43 of this chapter, and
  a copy of FAA Form 337 authorizing that installation is on board the
  aircraft.


14 CFR 43 covers MAINTENANCE, PREVENTIVE MAINTENANCE, REBUILDING, AND ALTERATION.

Basically, it needs to be an approved installation that is signed off and approved by the FAA using a Form 337 - MAJOR REPAIR AND ALTERATION (Airframe, Powerplant, Propeller, or Appliance).  The maintenance shop will take care of that aspect for you.

It is pretty common for delivering aircraft that need to cross the ocean, and there are even companies that specialize in it.  Really, your only option is to purchase an already approved kit because certification costs are so high.  

NBAA actually has a nice article which goes into more details, with lots of helpful links.