The MRS Control Module (that makes the airbags function) on my 2001 Mini CooperS (with only 66,000 miles on it) has failed and it’s going to cost me about $1,400 to get it replaced. Anyone have any suggestions as to how I might get this fixed without it costing so much? The dealer said it is really rare for the MRS to fail…lucky me. 
Just assuming it’s out of warranty? I once had a seat belt release seize on a 21 year old Honda, and the dealer charged $0 for the repair (“good will” repair). You could ask your dealer about getting a good will repair, all they can say is no. This is a safety item which is why you may have some ground to stand on.
Is $1400 the dealership quote? If so, You may try an independently owned import shop and see what they would charge.