For your income tax purposes, you use the date when the stocks left your control--you no longer owned them and could not call back or cancel the transaction, even if the charity records receiving them on a different date.
For example, if you requested the transfer at 6pm on Monday, after the market was closed, and the broker made the actual transfer 4:30pm (market close) on Tuesday, the date you record depends on the policy of your broker--when did the stocks leave your control so you couldn't cancel even if you wanted to.
