Without being demanding, what can I do to get my depressed grandmother to start taking an anti-depressant?

If she hasn't seen her doctor lately, she should. There are many antidepressants around and maybe she took this for awhile and felt worse. The drugs are tricky in that they take time to work, too. It's hard to get an elder to take them steadily, I know. Please try to get her doctor to make very clear that she needs to take them daily even if they don't seem to help. Or if they make her feel worse, ask him to try another type. If she simply won't take medication, then maybe the doctor can convince her how important it is to follow directions.
Good luck. You aren't alone.
Carol

thank you so much for the advice its so scary and sad to see her this way. i alwaysed remembered my grandma to be happy person!