The irony of dual deception
For one person to come up with a scheme is normal, but the fact that both of the young lovers thought of the same prank, that's downright ironic, because it means that they are extremely similar and probably compatible. They seem to have the same sense of humor.
The irony of love
Love doesn't make sense. The way it operates in the lives of those it bothers is funny and inconsistent and tricky. Somehow, the greatest force on the planet, true love, is also one of the most misbehaved, mischievous forces in the universe.
The ironic performances of their substitutes
The couple each hires a friend to stand in as them, giving their friends an opportunity to show what they really think of the couple. Their over-the-top and silly performances might be accurate, given how silly the idea was in the first place. Silvia and Dorante are just naturally sparky, ironic people, and so are their friends. The effect of the irony is light-hearted and fun.
The dramatic irony of Monsieur Orgon
One of the sweetest aspects of the story is that the father doesn't spare his daughter from the chaotic movements of love. He knows that he will be unable to save her from romance, so instead, he relishes the dramatic irony, knowing that ultimately, everything will work out perfectly.
The ironic second marriage
The first couple is a given, but the fact that Lisette and Arlequin fall in love is especially cute. The fact that even the ones who helped plot against marriage became the victims of a sweet one is ironic.