Gravity is a force. So the opposite of gravity will have to be another force.
Gravity is attractive. So the opposite of gravity will have to be repulsive.
Gravity is universal. So the opposite of gravity will also have to be universal. (Otherwise it wouldn't be much of an opposite would it?)
So we need a universal force which is always repulsive, and only dependent on the mass of the particle (like gravity).
Sadly, there is no such force which completely satisfies the above conditions. A few satisfy one or two conditions but they can't be called opposites then, can they?