I know it is sad to say this, but BRIBERY

Offer a point system where once they get 5 stars or stickers or stamps or slaps on the head or whatever, they get a prize. Sure it comes out of your pocket but it is better than teaching a lessons which just runs like a snail, and repeats what you did last week and the week before etc.
If that doesnt work you can be a hard teacher and dont teach them. Use the lessons to set out what you want for them again and allocate however many x minute piano study time chunks for the week. Continue that process till they can come and show you something the following lesson.
That may get parents pissed off becasue their money is for nothing, but they should realise it makes no difference at all! If they come to the lesson not knowing anything more than last week they might as well go home and work until they have something to show. That is what piano lessons are about! The teacher doesnt make them a pianist in the lesson, they just mould what work has already been set and done. People have to get that through their head and I've said this to many parents who call me up and are baffled, "Why did my child come home already?" They end up agreeing with me and i still have student who i have sent home come to me happily
It is how you do it, i dont take anything personal when they dont study but i say to them very clearly and without any hint of annoyance, there is just nothing we can do if you havent done what i set you. You dont want to have to teach them which note to press and which finger ALL the time. Some of the times ok, but all is just useless, they have to have at least something to work with.
and one last note. When you teach kids you should always be happy to teach them even if they dont do the work. Because I have taugh adults who told me when they where young they didnt do much piano etc and where forced, but now they regret not doing it. So it is the nature of children not to do the work! I have found all of my little students, and some older ones ahahha, enjoy getting prizes and reward for their efforts. I think anyone would enjoy that.