Interested in Language
Could you take a picture of us.
Could you take a picture of ours.
If you're asking somebody to help you take a picture that has you and your friends in it then number 1 is correct.
Sentence 2 is grammatical but its meaning is a bit different. When you say " a picture of ours" that means the picture belongs to you and someone else (for example, a friend of yours). A picture may belong to you but it doesn't necessarily have you in it and vice versa. You may see yourselves in a picture but that picture may not belong to you (or in other words, not yours!).