Cheyney Manor Barford st Michael, loads of roach, tench and carp.
Boddington res, fish beyond yatch club, roach, bream, tench and of course carp.
Manor lake Kirtlington, quality silvers, tench and bream (plus there are two other carp puddles).
Clattercote res, head to the far bank to avoid the carp but you'll still encounter a few.
Newlands Bents lake (nr Standlake), bream galore plus roach, tench and carp.
Pimlico farm, loads of silvers and carp, just avoid using maggots or the silvers will be small, very small.
Specimen lake at Nellbridge fishery (I think its open?), plenty of quality roach, rudd, tench and bream, use maggots.
Thenford lake nr Banbury, trout, roach, perch, tench, bream and carp.
Drayton Golf course, Warwick rd Banbury (just beyond Drayton secondary school), roach, rudd, bream (mainly skimmers) and carp.
There are no shortage of mixed fisheries BUT yes they all contain carp, though in the main very avoidable.