1) please don't be mad at me. let me make it up to you and take you to dinner, when are you free?
2) When are you free to let me take you out to dinner? Please forgive me
3) Please let me make it up to you and buy you dinner when you are free, please don't be mad at me anymore.
there are so many ways you can say it, personally i would take 1) because it sounds most natural. up to you. good luck