。
Could you perhaps specify a different date?
Literal
Different day [object-を] honorably-specify receive-could-not [question-か]?
ご指定いただけませんか is a highly polite request: ご + 指定 (specify) + いただく (humble receive) + potential negative + か. The negative potential (いただけませんか) paradoxically creates a more polite request than the positive form — 'couldn't you possibly...?' This is standard keigo for business contexts.