Simple answer: there is no documentation, other than a signed form 8332, that will convince the IRS to allow you to claim the child.
The one exception is a court order dated before 2009. From IRS Pub501: If the divorce decree or separation agreement went into effect after 1984 and before 2009, the noncustodial parent may be able to attach certain pages from the decree or agreement instead of Form 8332. The decree or agreement must state all three of the following:
1. The noncustodial parent can claim the
child as a dependent without regard to any
condition, such as payment of support
2. The custodial parent will not claim the child
as a dependent for the year
3. The years for which the noncustodial parent,
rather than the custodial parent, can
claim the child as a dependent
The noncustodial parent must attach all of
the following pages of the decree or agreement
to his or her tax return
• The cover page (write the other parent’s
social security number on this page)
• The pages that include all of the information
identified in items (1) through (3)above
• The signature page with the other parent’s
signature and the date of the agreement
