Your original problem is caused by not reporting the 1099-C on your return, but the IRS instructions don't explain how to report the 1099-C in the situation where the other ex-spouse has agreed to pay the tax, so I'm not sure what you would have done originally to prevent this.
I can offer a suggestion but don't know how the IRS would view this. report the 1099-C
and then as a negative adjustment on the other income schedule enter "less debt cancellation above reported by ex-spouse XXX-XX-XXXX. (or similar wording with their SSN)
