Parodies often achieve their effects by exaggerating certain features of the original work in a humorous way. Another feature of Romeo's impulsiveness is his running recklessly into danger: In the first act he secretly attends the party for Juliet, in the second act he tears his flesh climbing into the orchard to see Juliet, then in the third act he rushes between Mercutio and Tybalt, rushing headlong to Friar Lawrence where he flings himself onto the floor crying and "babbling." Finally, he hears a rumor of Juliet's death, rushes out to the apothecary, bribes him into selling his poison; in the final act, he charges into the Capulet tomb, assumes Paris is there to do ill, kills him, and then flops down beside Juliet, moaning her death, and drinks the poison to kill himself.
To parody these impulsive actions, you could have Romeo spinning off from place to place with reckless abandonment and no rationality to his actions. Cuts and bruises mount up on him, but he pays them no regard. (You have seen similar mocking scenes on Saturday Night Live, I am sure. One such example was a parody of Julia Child by Dan Akroyd who cut "her" finger severely, but continued to prepare a chicken with blood spurting everywhere in ridiculous amounts.)
Are you writing a paper or a short response? If you are, you could make Romeo the bachelor on a show like The Bachelor. Make fun of Romeo's being so in love with Rosalyn at the beginning of the play that he is sick and then mock how he quickly gets over her and falls in love with Juliet at first sight.
A parody is mainly a funny or mocking imitation of a work. Use exaggeration--perhaps have your Romeo fall in love with every woman he sees (young, old, ugly, etc.). Just as the bachelor on the TV show claims to be in love with several women at the same time, you can have Romeo in the "confession room" talking about how he just can't control his emotions or impulsiveness.
I hope this helps.
There are so many parodies on current TV, that you could create a reality show based on Romeo's impulsiveness that would have him fall in love with every girl he meets then at the end of each show he meets someone new.