I would appreciate your responsiveness ? evtl.

I would be grateful if you could oblige.

Without more context, maybe just something like

I would very much appreciate ...
... anything you can do to help.
... whatever you can do to expedite this request.
... your cooperation / assistance (in this matter).
etc.

The last two actually sound rather stuffy to me; I would personally just say 'anything you can do to help.'

If you've made a mistake or missed a deadline or something yourself, you might say instead something like

I will deeply appreciate ...
I will be very grateful for ...
... your patience and understanding.
... your willingness to work with me on this.
... your help in resolving this problem.
etc.


'Oblige' is now rather old-fashioned, and 'responsiveness' isn't the right word; it's usually used when there's a degree or spectrum that can be judged or measured, e.g.: the responsiveness of the steering in the new sports car; the responsiveness of the tumor to the new medication; the responsiveness of Iowa voters to the latest ad campaign.

Das Problem mit dieser Anfrage ist das Wort "Entgegenkommen". Das Wort bezieht sich meist auf eine Verhandlungsposition. Der Schreiber erbittet, wenn er zahlungspflichtig ist, eine für ihn günstigere Vereinbarung vom Adressaten. Das kann sich auf
-- die Verminderung der zu vereinbarenden Summe,
-- auf die Stundung einer fälligen Zahlung / die Vereinbarung einer Ratenzahlung,
-- die Erweiterung einer vereinbarten Leistung (z.B. späterer Auszugstermin) oder
-- irgend etwas anderes für den Schreiber günstiges
beziehen.

Vorschläge:
"I would really appreciate if you could find a way to accommodate me (in this matter)".
"I would be very grateful if you could find a way to make the concessions I have suggested / as suggested."

Ah, thanks, that helps. AndreasS's suggestions look perfect, then, except that I would say 'appreciate it if.'