A dynamic character is one who goes through a change throughout the course of the story. The first character who could be considered dynamic is the Nurse. In the beginning of the play, Nurse seems to be totally on Juliet's side, and, although she does sometimes act as Juliet's mother, she also acts as her friend. Once Tybalt is killed, the Nurse begins to change the way that she acts around and responds to Juliet. She then tells her that she should forget Romeo and that Paris might be the better man for her. A second dynamic character is Lord Capulet. Capulet is a very strict man who, in Act 3, seems to treat his daughter with no compassion or feelings when he tells her that she either will marry Paris or suffer the consequences. Once he thinks she is dead and when she actually dies, he shows a completely different side, showing complete care and compassion for his deceased daughter. By the same token, Lord Montague can be considered dynamic in that he HATES the Capulets but by the end of the play, he and Lord Capulet reconcile their differences and erect a statue of Romeo and Juliet in their honor. A final dynamic character could be Romeo; even though he does not change in many ways, he does go through a change in his character. The beginning of the play introduced a sad, half-hearted Romeo but once he meets Juliet, he becomes happy and wants to live a wonderful life with her. Although he does die in the end, he dies knowing that he can not be with her because he has died, not because he is banished from her.
I think dneshan is correct in identifying Lord Capulet as a dynamic character, but way off the mark as to why. Lord Capulet shows himself to be a fairly enlightened individual when it comes to marriage. He tells Paris straight out that he must win the favor of his daughter, that his will is only a part of the deal. Many have speculated that his own match to Lady Capulet was enforced and that as such, it is not a happy marriage. Regardless, Capulet puts his daughter's happiness first. That goes out the window once Tybalt is killed and Juliet begins grieving (grieving for Romeo's banishment and not her cousin's death). Capulet decides the best remedy for this is to marry her off to Paris, an event which he assumes which will make her happy but which badly backfires. Yes, he changes again when he believes his daughter has died, but that is the backwards way around this argument. If you need further proof of his benevolent nature, look at the way he deals with Tybalt during the party scene.
As to Montague, he is too minor a character to consider for this problem. Romeo, Juliet, Nurse, Capulet and the Friar are the only characters you can consider for this problem. Tybalt never changes, nor does Lady Capulet, and for that matter neither does Mercutio. Benvolio is steady throughout; a nice character, but without change. The Prince only regrets his leniancy in the first place. I would put my work into Romeo (the most fully detailed character in the play and the one who has most growth) Capulet, the Friar and Juliet. The Friar is a great character. He's trying to do good, he's trying to bring peace and fix a problem which has long plagued this city, but he royally screws up.
As a back up plan I would look at the Nurse.