Most stations on the Atherton line (including Ince) are ruled out by having at least a couple of trains per day running to either Wigan NW or Manchester Piccadilly - except for Hag Fold.
From Hag Fold you always need to change twice, either at Salford Crescent/Piccadilly, or Man Vic/Picc or Wigan Wallgate/NW in the current timetable.
Three small shacks between Wigan & Southport - Hoscar, Bescar Lane and New Lane - fall into the same category as the Wigan-Kirkby line, since current timetable has no trains stopping at these which go direct to Manchester Piccadilly: so it's change at Salford Crescent/Piccadilly, Man Vic/Picc, or you could go the slow way via Southport/LSP.
In reality, for all four examples above, you could easily change at Wigan, which can be similar or shorter walk train-to-train than at some large interchanges like Liverpool South Parkway or Manchester Picc (P.13 to main station) - but we're not allowing out-of-station transfers for purposes of this thread.
With the four stations above, the "at least 2 changes" situation is a result of quirks of the stopping patterns in the current timetable rather than any inherent railway geography. So a 1-change facility might be restored at any of these by some future stroke of a timetable planner's pen (or more likely a click of her mouse).
As
@DanTrainMan185 commented, this topic comes up regularly every year or so, and usually Denton & Reddish South are on the list. These stations aren't applicable at the moment, but if the southbound service to Stockport disappears in a future timetable iteration, they'll be back.
