I appreciate your kind cooperation.
Thank you very much for your cooperation.
I pray you.
お願いです
Sorry to inconvenience you but I appreciate your help.
I appreciate your kind cooperation.
You will please exert yourself in my behalf―I leave my affair in your hands―(初対面の挨拶なら)―I hope we shall have a good time together.
Yes, please.
Thank you very much for the consideration you will give to our request.
I'll leave that up to you.