I think the best example is a pun. Puns are plays on language that are used intentionally for laughs. In this play in particular there is plenty of raunchy language, but there are also other puns. Consider this exchange between Romeo and Mercutio:

ROM:

I dreamt a dream to-night.

MER:

And so did I.

ROM:

Well, what was yours?(55)

MER:

That dreamers often lie.

ROM:

In bed asleep, while they do dream things true. (enotes pdf. p. 27)

In this case, the play on the word “lie” is humorous and clever. Dreams “lie” as dreamers “lie.” While this is funny it is actually thematically important, as it stresses the lies in dreams. Romeo and Juliet choose to pin their hopes on a dream, with tragic results.

The Nurse is certainly the most bawdy of the characters and her sexual innuendoes delight the groundlings, especially. Then, too, her frivolousness in the most serious of moments is annoying to Juliet, but amusing to the audience. The scene in which she enters with her servant Peter and Mercutio jokes that her layers of clothes are sails is great comic relief.

Reread any lines by the Nurse and you will find many examples of humor, as she is one of the major elements of comic relief in this play. Her lines often use the literary device of repetition to create humor; I also recall her use of a metaphor to compare Romeo to Paris. She calls Romeo a "dishclout," though Juliet is not amused. One other spot where you will certainly find plenty of comic relief using literary devices is when Romeo is moping around and wallowing in his unrequited love for Rosaline. Plenty of comedic material in his speech with Benvolio, and most of it uses figurative language. 

If any character is a clown, it is Mercutio. Throughout the play, Mercutio functions as a source of comic relief. Usually, Mercutio adds humor by lampooning Romeo. In contrast to Romeo’s serious and idealistic romanticism, Mercutio is practical and irreverent. Mercutio frequently reduces love to physical and sexual attraction, and this is funny because it contrasts with Romeo. While Romeo pursues his hopeless relationship with Juliet, Mercutio points out the ridiculousness of the situation by trivializing Romeo’s feelings. In addition, Mercutio makes clever use of puns and general wordplay in order to get these points across. There is rarely an instance in the play in which Mercutio is not speaking in euphuisms, and it makes for very witty dialogue.