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@mrosenb515 wrote:

...I have two dependent college students who took distributions from Coverdell ESAs in 2019 under their Social Security numbers. But we want to claim the AOTC under parents' SS numbers. We withdrew $4,000 per student less than the maximum so we could file for the maximum AOTC....

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You can't plan it this way.  Education benefits are all coordinated.  No double dipping is allowed in any way.

AOTC is always on the first $4,000 incurred.  Qualified education expenses eligible for excludable distribution from ESA must be reduced by any such expenses on which AOTC is claimed.  It does not matter whether the account is under the student's or parent's SSN because both AOTC and ESA are with respect to the student.

What you can plan is to determine whether it is more beneficial to forgo AOTC in favor of ESA or to claim AOTC on the first $4,000 and ESA on the balance.

Be careful with this as there is a due d penalty attached to this provision.