How do I stop an old rocking chair from falling over?

I'm not sure if I understand the question Jean. Are you wanting to change the rockers so they don't rock?

Don't worry, its very hard to flip a rocker. Regular chairs are much easy to flip.

Is it a conventional curved runner rocking chair, or a 'slider platform rocker'? The latter style were a huge fad decades ago, but yes, they did tend to tip over backwards easily, especially when weight was applied to the top.

Hi Jean. I'm Cindy. If you wrap rubber bands on the ends of the rounded bottom rockers, they will stop the rocking. Good luck Jean and Happy Thanksgiving.

ThInk you so much. I can do this! Happy Thanksgiving to you Lso.

Regular wood rocker.This old farmer I know put a board across the bottom of the rockers in back I think it was 2x2 he used more 2x2 cut in pieces attaching them to board then onto rockers with bolts. So when you rocked you could only rock so far back. He had 4 big rocking chairs on his porch in front of big window & did not want any of his grand kids going backwards thru glass when they got all silly on them. If it's a glider type maybe the base is on backwards sometimes when they get assembled or refinished they get put back together wrong. Longest part of base should be pointing backwards. In these pics it's wrong https://www.hometalk.com/diy/paint/furniture/q-rocker-back-and-tipping-4360203