Can I be cheeky and nominate Cranbrook and Newcourt stations? They do fulfil your criteria - they're currently open stations, and they've always been unstaffed. (Even if they've not been open for that long in the grand scheme of things!)
Longcross.?
If a station has re-opened unstaffed and remains so, but was staffed historically before being closed- does it qualify? If so, most new/reopened stations could appear on this list.
One round here I can think of that has ALWAYS been unstaffed is Glasshoughton.
In the South East (as far as I know)..
Swale
Three Oaks
Doleham
Longcross.?
Lake (Isle of Wight)
Do you include station platforms unmanned but tickets issued from adjacent signal box/crossing box (all of which are now closed !) such as..
Southease
Normans Bay
Faygate
and pre 1997 Waddon Marsh and Beddington Lane
Not sure about other SR "halts" (steamybrian has listed some) - there's others like along the south coast like Pevensey Bay, Aldrington, Fishersgate, East Worthing, Fishbourne, Southbourne, Nutbourne, Bedhampton, Hilsea - and Holton Heath? - plus Polsloe Bridge and St James' Park. I think some of these may have been staffed at some time (or may be now, it's a long way from here!)
. .......
Not sure about other SR "halts" (steamybrian has listed some) - there's others like along the south coast like Pevensey Bay, Aldrington, Fishersgate, East Worthing, Fishbourne, Southbourne, Nutbourne, Bedhampton, Hilsea - and Holton Heath? - plus Polsloe Bridge and St James' Park. I think some of these may have been staffed at some time (or may be now, it's a long way from here!)
Was the original Connon Bridge not staffed?Golf Street
Connon Bridge
Willington and Matlock Bath; both closed and then reopened.
All of the current stations along the S & C with the exception of Settle and Appleby.
Wasn't Kirkby Stephen once staffed?
I'm not sure that Kempston Hardwick or Aspley Guise ever had station staff, as such.
Kempston Hardwick was destaffed in 1968
Apsley Guise still had a crossing keeper until 2004 but the following web site illustrates BR tickets issued from it..
http://www.disused-stations.org.uk/a/aspley_guise/