To keep someone sweet is to give the impression the person is on your good side/ good books for the intention of gaining something from them in the future or to avoid drama or conflict.
Person 1: Joe is a backstabber, watch out for him.
Person 2: Don't worry I'm keeping him sweet till he gets us those tickets for the game on Saturday.
Example 2
Person 1: Are you inviting Joe's ex? He might get mad.
Person 2: no, I'm keeping joe sweet, when he loses his shit he wrecks the place.
Keep sweet