Tax Deduction

Ok so here is the scenario, I have been divorced since September 2001 in the State of Georgia. My divorce was settled out-of-out through a mediation between our two attorneys, and a lot of back and forth. At that time, I thought I would be FAIR, and give my X one tax deduction for one of our three children, since the state court can not force the custodial parent to do that. Since that date, things have changed and my X has now moved out of state, and barely sees the kids. I have found that due to the decreased amount of child visitation; my expenses for childcare have gone up, etc. etc. That tax deduction would sure help with some of these expenses. So with that being said my question is, I know the State of Georgia does not deal with tax a deduction since that is a federal matter, but how would I go about getting that tax deduction back, or can I? Obviously there is a change of circumstance, but I am not sure if I have any recourse, and if I do what is it? Any one?????