How can I get floor paint to stick better on our outside stairs?
Peeling paint is caused by poor adhesion to the underlying surface. For stone and concrete a professional would recommend grit/sand blasting. This ensures removal of all surface contaminants which could affect adhesion.

If you insist on doing it yourself: remove all existing paint, wire brush entire surface, wash surface with mild acid solution (we use pool acid called Muriatic Acid, it is actually weak hydrochloric), rinse clean and dry. Use a high quality outdoor concrete coating and apply as directed by the manufacturer's instructions using high quality applicators (brushes &amp; rollers). Some of the epoxy coatings do not require a primer. Do not use an additive unless directed to by the manufacturer.

It has been my experience that you will find the best coatings (and advice) at a paint shop or commercial/industrial supply house, rather than at a "big box" store.