Sorry I am a bit late responding I needed to get 2nd and 3rd photos. Obviously imho all the above advice is top shelf as always. What winches are you talking about? Cabin top for halyards etc or coaming mounted for kite brace and genoa/kite sheet winches? Both need good structure under them as well as adjacent structure and structural continuity.
We bought a 9.3m racer/cruiser ~8-9yrs ago with the genoa and kite brace and sheet winch mounted on top of the coaming as below - apologies for poor photo resolution - clearly it is a self tailing winch with added cam cleat below it for belts and braces security.........and it was obviously no good at first sight with winch base outer diameter overhanging the coaming width. The usual design arrangement is a column / post design in the coaming at that winch landing of diameter a bit greater than the outside diameter of the winch base max outer diameter, and suitable coaming structural scantlings including under the coaming if needed. Sorry for stating the obvious.
On our yacht there was no structural stiffening under the coaming. When on pick up we sailed down the coast to the harbour the coaming flex was more than a tad alarming.........and first rectification task on the list.

So we added as in the below photos the under coaming top ply pad and lateral stiffening ply gusset, with timber sections added to avoid buckling of the ply free edges and gain structural continuity to the adjacent grp laminate. See a bit tapered ends of the timber sections to avoid a stress concentration at their ends. In hindsight I should have put on more of a taper. Epoxy glue, vinylester gelcoat coarse sanded, acetone cleaned then glued.
I fully realise that the whole additions are as rough as a bear's rear - so please don't comment on that - I will improve the aesthetics soon.................including Norglass Ship Shape painting............