Great question. The process is not be simple but after a few steps you may
be able to get a one-time smog exemption, but you must be Income Eligible,
meaning have low income. The next time the DMV asks for a smog check you
will have no choice but to retire the vehicle to the state for $1000.00,
assuming the program still exists in two years.
The process you'll need to complete is first applying for CAP (consumer
assistance program). CAP will pay the Gold Shield certified smog check
repair station of your choice $500.00 to repair emissions related faults. I
know you mention you think the problem is carburetor related, but let a smog
check station diagnosis it. They may find other problems as well. If the
vehicle still fails after $500.00 in repairs, you'll have the option of
paying the rest yourself to complete repairs, or you can ask for a smog
check waiver (if you're low income).
If you ask for a waiver you'll need to make an appointment with the state's
smog referees office. A state smog referee will inspect your MGB and find
out why $500.00 was not enough to get your car to pass the emissions. If
his/her report concludes the repairs conducted were in fact needed, and the
vehicle needs further repairs which you can not afford, they will give you a
one-time waiver.
In this specific case there's a small possibility that you might be given a
waiver solely on the fact that your vehicle's carburetor is no longer
manufactured and/or available for sale. Good luck.