First, I would actually argue that the balcony scene is not really calm. It's actually a very emotionally intense moment. Romeo is overcome with his passions, and Juliet, while she tries to remain level-headed at first, gets swept away in Romeo's intensity. So the lighting will have to reflect intense passion. However, the scene certainly takes place on a summer night, which can create a peaceful mood that contrasts with the intense emotions. So the setting will have to reflect the darkness and peacefulness of the moment in the garden, while the lighting will have to reflect the different emotions.
Colors are very important when using lighting to create mood. Colors we might want to consider using are magenta, which can be "warm and romantic"; lavender, which can be "restful and soothing"; pink, which can also be used romantically; and also possibly yellow, which can can be "cheerful"(Iacobucci, "Stage Lighting Basics"). We can even combine colors to create just the right the mood.
To capture the darkness of the night, we'll want to create a setting with a dark backdrop, possibly painted with stars and a moon. The rest of the setting would have to include items to make it look like a garden, including trees, shrubbery, and a garden wall, plus a balcony. To reflect the fact that it is also a summer night, we could use a yellow-white light reflecting on the general stage area. We know that it is summer, because in the third scene Juliet's nurse asks when Lammastide is, which is a festival that takes place in mid-July and is also when Juliet was born.
When we first see Juliet in the balcony scene, she is feeling very pensive; she's reflecting on her problem of love when she says, "Ay me! ... O Romeo, Romeo! wherefore art thou Romeo?" (II.ii.26, 35). Therefore, at this moment, we'll want a softer color shining on Juliet, probably lavender with a touch of pink. Romeo, on the other hand, is feeling much more intense. He is feeling very lustful when he compares Juliet to the moon, telling her to cast off the moon's virginal uniform, as we see in the lines:
Arise, fair sun, and kill the envious moon,
Be not [the moon's] maid, since she is evnious.
Her vestal livery is but sick and green,
And none but fools do wear it. Cast it off. (5-9)
In these lines, "vestal" means virginal while "livery" refers to clothing or a uniform. Therefore, when Romeo, in his mind, tells Juliet to cast off the moon's "vestal livery," he is telling Juliet to cast off her maidenhood, the ultimate sign of passion and lust. Therefore, we need more intense colors reflecting on Romeo, such as magenta.