I would be very careful with negging if she is feeling down, she may take it the wrong way and go nuts at you. Also I would try to avoid being the guy to comfort her chances are this will land you straight in the friendzone, with the line "its great I have friends like you" being almost guaranteed.
I think your best bet is to invite her to something you are doing then just go from there with standard game. It sounds like she is a friend or someone you have known for a while if so you could make it nice and casual by saying something like "you have been down lately, you should come along to (insert event) to cheer you up a bit" or something similar.
Hope this helps
