Which is proper? 'Their' is singular.
"Friends" is correct, since the subject is plural. "They are (their) friends" or "they are (his) friends". The pronoun is an adjective here and doesn't influence agreement.
You can see this also by the helpful writing practice of flipping the sentence around "their friends are you and I." (Note that "I" is correct here because it is nominative. But some linguists suggest that the I-me distinction is disappearing and even good writers often don't bother with it.)
As @John_Lawler says, most speakers with use an idiom to navigate any ambiguity. But "You and I will be their friend" is also idiomatic, and frequently used to suggest a joint effort to help someone who needs a friend.
"You will be their friend." You is both singular and plural. Here, it is singular.
"I will be their friend." I is singular, so you will be just one friend to them.
"You and I will be their friends." Notice the plural subject (You and I) and the plural object (friends).
Their is a possessive pronoun. Apart from using it to relate to certain people, animals, or things, you could use it to refer to a single person whose sex you do not know or wouldn't specify.