It is possible for the title of a work to be a paradox, but the idea doesn't really apply well here. A paradox is a particularly strong contradiction, one that is essentially logically impossible. Leaving a raisin in the sunlight would be striking. It is a good image, and a metaphor, originally from Hughes' poem "Harlem." However, it would not be a paradox.
Instead, look at the stage directions for the very first scene of the first act. We're told that the family's living room would be "comfortable and well-ordered" if it weren't for the "indestructible contradictions to this state of being."
That's a paradox, and one that would be almost impossible to stage. The rest of that first long set of stage directions explains what this means, but to be honest, the audience is not going to see this. This paradox is for the reader (or the director) to strive toward.