in a way that is useful to you because it saves you time or does not spoil your plans or cause you problems:
Conveniently, her parents are often willing to babysit.
At that time, ice cream couldn't be conveniently bought in a store.
in a place that is close or easily reached:
The hotel is conveniently located near the airport.
if someone has conveniently forgotten, ignored, lost etc something, they deliberately do this because this helps them to avoid a problem or to get what they want:
You conveniently forgot to tell me she was Nick's sister.