From card games relying on making or ditching books or tricks, such as Hearts or Spades. In a making game, for example, if you are holding all or most of the desired cards in a given suit (hearts, spades, diamonds, clubs) then you can be fairly sure of taking a high number of 'books' or plays.
Get Melanie to talk to her for you... Diplomacy's always been her strong suit.
The phrase derives from card games where suits are considered to have different values.
Fred: Dancing isn't my strong suit. How about we go bowling instead?
Interviewer: We'll let you know.