The current rules require all vehicle owners to provide a CURP number. I just bought a car - there is no way around this. To obtain a CURP, you must have a residency visa, either temporary or permanent.
In the past, I believe that non-residents could get a generic CURP from your bank or some other source if you needed one, such as to open a bank account. These non-INM (immigration) issued CURP's would have questionable legality.
In my case, I had to produce a residency card.
As we know, the new rules require that tourists entering Mexico with foreign-plated cars must exit the car from Mexico as they themselves do before six months. There are likely thousands of foreign-plated cars "trapped" in Mexico because they are illegally plated and would be subject to stiff fines to get them out of the country.
One option for those in your situation is to transfer ownership to a Mexican national who would "own" the car for you. There may be, because of the documentation of the vehicle, be some
problematic issues. Maybe insurance issues too.
Be sure to visit www.lamanzanilla.info for more information about La Manzanilla Mexico.