Claiming Children on Taxes

My question is regarding child tax credit. In 2009 my ex and I had written into our custody agreement that he would claim my son on taxes and I would claim my daughter.

In 2010 we re-wrote our custody agreement to address custody but left out the issue of taxes. I pay child support, as well as extra-curricular activities for the kids. Since the most current agreement regarding custody of the children does not address taxes, does the issue of who gets to claim which child default to the previous order? If it does not, who is eligible to claim the children?

I would need to see the agreement to determine if you modified the entire agreement or only the portions that changed. If it is not covered now, the credit is given to the parent with custody for the majority of the time. If time with both parents is equal, then you need to read the IRS publications which give further instruction on the credit.