You may be able to take the Hope or lifetime learning credit in the same year the beneficiary takes a tax-free distribution from a Coverdell ESA, provided the benefits are not determined on the same education expenses.
In this case, you would have to reduce your adjusted qualified education expenses by the amount taken into consideration in figuring the Hope or lifetime learning credit:
Total qualified education expenses
Minus tax-free educational assistance
Minus expenses taken into account in figuring the Hope or lifetime learning credit
Equals adjusted qualified education expenses
Once that calculation is done, you can take your adjusted qualified education expenses, and the amount of the distribution you received, and calculate the taxable portion of the earnings in that distribution using the calculation indicated above.
Qualified Tuition Program Disbursements
If distributions are received from both a Coverdell ESA and a Qualified Tuition Program (529 plan) the same year, and the total amount received is more than adjusted qualified education expenses, the expenses must be allocated to the distributions to determine how much of each is taxable. You can allocate your expenses in any reasonable manner.
For example, the year in which a beneficiary graduates from high school and enters college, a vocational school, or other postsecondary school, and has qualified education expenses for both, the Coverdell distribution may be allocated in part or in total to cover any high school expenses, since these are qualified expenses for purposes of the Coverdell ESA but not for the Qualified Tuition Program. The remainder of the distributions could then be allocated to postsecondary education expenses, which may qualify under both plans.