Depends on how far apart they are when the lower aircraft asks for climb, depends on the type of aircraft it is (A340 or something with a similar climb rate) and how busy I am.
If I'm busy then the plane will probably wait, unless I have a need to vector it for something else which would fit in with climbing it against the other aircraft.
My immediate reaction would be to wait until they've passed, but if there's other conflicting aircraft behind the first one then it may not get a climb at all - if I've got to put four or five aircraft on headings to climb one then it may not be worth it. If it's a safety reason, like icing, then of course it will be done as soon as I can accommodate it, if the pilot just wants to save a few quid then iot will be done when and if I have time.
That probably doesn't make much sense, but without seeing the exact situation I couldn't say what I'd do. It's the usual situation of asking 10 controllers what they would do and getting 11 answers back. The trick is to keep your workload as low as possible whilst still giving planes what they want.