Getting a business-card after jumping from a sky-scraper I remember seeing either a trailer for it or a part of the first episode. 

There was a guy who tried to commit suicide (I think) and jumped off a tall building. As he was falling this guy and I think 2-3 others kinda fly next to him. 

The guy offers him his services to save him or something coz I remember him giving the suicidal guy a card. 

Sorry if I didn't describe it very well, but that's a that I remember.
I believe you may be looking for Noragami.

The scene you described is in episode 4, where a guy tried to commit suicide by jumping off a rooftop.

The only part that doesn't fit your description, is that the guy jumped. He intended to jump, but "accidentally" fell instead.