One good place to start finding oxymorons in Romeo and Juliet is Romeo's first longer speech in the very first scene.
One example is "brawling love." While it may be true that lover's quarrels can be frequent, fighting, or brawling is a contradiction of love. Likewise, there is a contradiction in the phrase "loving hate." Hatred is the exact opposite of love, therefore the combined term is an oxymoron.
Also in this speech, another example of an oxymoron is "heavy lightness." Lightness cannot be both heavy and light. Romeo is using this phrase to define his interpretation of love and his definition continues with the oxymoron "misshapen chaos." Chaos has no shape; it is a state of utter confusion and disorder, therefore chaos cannot be "misshapen." To be misshapen is to be "badly shaped" or "deformed" (Dictionary.com).
Another good place to find oxymorons is in Act 3, Scene 2, when Juliet first learns that Romeo has killed Tybalt. Juliet refers to Romeo as a "fiend angelical!" A fiend is another word for Satan or the devil, or a cruel, wicked person, while angelical is an adjective describing one who is like an angel, or virtuous. A fiend cannot also be an angel, therefore the phrase is an oxymoron.
Why then, O brawling love, O loving hate,
O anything, from nothing first create,
O heavy lightness! Serious vanity!
Mis-shapen chaos of well-seeming forms,
Feather of lead, bright smoke, cold fire, sick health,
Still-waking sleep, that is not what it is!
This love feel I, that feel no love in this.
Act 1. Scene 1. 175-182
Good night, good night! parting is such sweet sorrow,
Act 2. Scene 2. 184
Beautiful tyrant! fiond angelical!
Dove-feather'd raven! wolvish-ravening lamb!
Act 3. Scene 2. 75-76
A damned saint, an honourable villain!
Act 3. Scene 2. 79.
Thats all I can find. You can split the first one up into two since it is so long. Good luck!