お手数ですがよろしくお願いします
Sorry to inconvenience you but I appreciate your help.
I appreciate your kind cooperation.
I am sorry to trouble you, but I appreciate your support.
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.
Thank you very much for the consideration you will give to our request.
Thank you very much for your cooperation.
I would appreciate your kind guidance.
I apologize for the trouble this will cause you, but I appreciate your kind cooperation.
I beseech your favor.