When I use the word "curse" I suppose I mean a vindicatory action imposed on you from another. You know that term they'll get what's coming to them. That sort of thing. I had this friend, I was really good to. She betrayed me. A week later she hit a curb and busted 2 brand new tires. Was it karmatic or coincidence. I would like to think it was karma, but I don't know. I think it's an interesting conversation to have.
Note the part in bold. Who is the "other" you refer to? In the example you give, where your friend suffered an accident shortly after betraying you, are you saying that you may have imposed vindictive action upon her? Or that it was imposed upon her on your behalf? If so, by what means?
Coincidence is just that, but karma assumes a supernatural agent of some sort. A curse, by your definition, requires action from some external force or being that we cannot detect aside from the results. And we would have to accept that it is a capricious and/or deliberate actor, since there are people who get away with doing harm to others and they may even profit from it.