My neighbour had a repair guy fix and paint his stairs. (25+year old IG vinyl lined pool, concret deck all 'round') This was done 3 yrs ago.
The pool was drained to below the bottom stair tread. The repair guy drilled 3/8" holes in the "flexing stairs" about 4 / step spaced evenly. Thru the holes he sparyed / filled the space below the stairs with expanding foam. the foam expands and oozes out the holes. Told me he had to be careful not to over fill else it could buldge the stairs. Next day, cleans up the holes, then mixed up some Polyester resin and glass fibers, fills the holes. Sands and paints using Gel coat (polyester 2 part paint). The steps are still fairly solid, although i've not been in the pool to test em in the past 2 yrs. Seems a decent solution to me.