What type of pet does Juliet wish she could make of Romeo and thus keep him near her?
In Act 2 Scene two, she says she wishes he were a bird on a string so that she could have him gone no farther than "a wanton's bird, that lets it hop a little from his hand like a poor prisoner...and with silken thread plucks it back again." She wishes to let him fly, but not far--when he gets too far, she wants to be able to pull a silken thread to draw him back.
Romeo is willing enough to be her "bird", telling her " I would I were that bird". Yet Juliet withdraws her request, saying that she fears she would kill it with too much cherishing. It is an apt metaphor. Children's birds, being tied to their wrist and pulled down at will (sort of like a helium baloon), didn't live very long and, as it turns out, neither will Romeo. Although it is not the cherishing that kills him, exactly.
In Act II, Scene 3, Juliet says,
"'Tis almost morning, I would have thee gone-and yet no farther than a wanton's bird, That lets it hop a little from her hand, Like a poor prisoner in his twisted gyves, And with a silk thread plucks it back again, So loving-jealous of his liberty."
This takes place after they spend the night together and Romeov has to leave for Mantua. Juliet says she knows that he must leave, but she would like to keep him as a bird and when he wanders off too far she could just reel him back in again to keep him close to her.