Is there a specific supplication or remembrance (dhikr) to be said when giving charity, other than "O Allah, accept this charity from me"?

There is no specific supplication that the giver of charity should recite when giving it, but it is sunnah to say "Bismillah" (in the name of Allah) when giving it. The giver of charity should not hope for the supplication of the recipient, lest the reward of the charity be diminished. If the recipient does supplicate for him, it is recommended to return a similar supplication. If a Muslim gives pure wealth for the sake of Allah, Allah will accept it from him, and he should strive to ask Allah to accept his deed and to overlook his shortcomings.