Can't get the dates of matches at the moment, put I can give you any result from the Southern League from the 1909-1910 season up to 1992 - 1993 and Southern League Cup too. I may be able to track down individual dates for matches, but may take longer and can't promise faithfully!

In my never-ending quest for obscure football results, I stumbled upon

http://nonleaguegeek.co.uk/

which seems to have Southern, NPL, and Isthmian results (premier div only) back to mid-1980s - just the years I miss out of the Times archive. And as bonus, there are FA Trophy fixtures AND dates (not for all seasons though).

Upon closer scrutiny:

NPL complete back to 1979/80, but must be accessed via individual clubs rather than through tables, which don't work.
Southern complete back to 1984/85 (1983/84 being added), tables work.
Isthmian complete back to 1984/85, tables work.