Another idea I read about is to launch, rendezvous, and set up a large reflective mirror that concentrates sunlight on the asteroid which would heat it up and cause out gassing which would deflect the orbit ever so much. The mirror could be made out of light weight mylar film. If it's tumbling at a fast rate I don't know what you'd do.
Comets outgas. Do meteors do so, also? I thought that they were mainly composed of iron and nickel.
Which is susceptible to magnetic influence. Hmm. I wonder if there will eventually be some practical way to use that to deflect it.