Romeo and Juliet is made up of coincidences.  First, we see that Romeo is not at the opening fight scene because he is depressed over Rosaline.  Normally, he would have been with this group and might have been injured.  Romeo also meets Juliet by chance.  A servant is given the task of distributing invitations but he cannot read.  He happens upon Romeo and asks him for help.  Otherwise, Romeo would not have known about the party where he meets Juliet.  The chances continue until the final chance where Romeo commits suicide, missing Juliet's awakening by moments.

I would have to agree that one large coincidence is the fact that Romeo is on the "rebound." he may have not fallen for Juliet so swiftly if he his one-sided "relationship" with Rosaline had not just ended. He is looking for someone who will, and can, return his love. Fortunately for him, Juliet is there.

When I think of "coincidence" in Romeo and Juliet, I also think of misunderstandings or miscommunication. There are so many times in the play that an impulsive act results in death because of lack of communication. In that case, that could mean that the characters had more control over their actions than thought. The problem with the word "coincidence" might be that it should really be substituted with "Fate". When does Fate intervene and when does it not? The Prologue is clear when it says that these two lovers will not find a happy ending, so no matter what they do to stay together, by pre-destined fact, will not help them.  So, I'd say first, Fate messes with them the most, thereby creating the illusion of coincidence.

  One could argue that if Rosaline had not rejected Romeo, he wouldn't have been sad so he wouldn't have gone to the party to meet other girls.  Then, it could be said that Romeo's choosing to fall in love with Juliet was a coincidence because there were other girls there at the party. Next, had Tybalt not wanted revenge, then the fight wouldn't have happened. One last major coincidence was when Friar John wasn't able to get the message to Romeo about Juliet faking her own death. He was held up by a quarentine in the house that was beyond his control. Had he been able to get the message to Romeo, then the  lovers wouldn't have died.

Look at your assignment and narrow it down as needed.  That is a big question.

The first coincidence is that Romeo is on the rebound, as they say, from his former girlfriend when he first meets Juliet.  This might make him more susceptible to her charms.  The fact that he goes to the party is also a coincidence.  When he sees Juliet, he does not know who she is.  You could consider it a coincidence that he falls in love with a Capulet.  In the grander scheme of things, the fact that they are from feuding families is a coincidence also.