British Airways will tell you that they already serve MAN-JFK daily: the flight numbers are BA1552 / BA1553. Of course, this flight is otherwise known as AA210 / AA211 operated by BA's Oneworld partner American Airlines. Given that this codeshare operation already exists, would BA consider potentially diluting the market with a second (or replacement?) schedule on their own metal? With MAN neatly functioning as a spoke for AA but representing a bit of a logistical headache for a 're-based' BA long-haul aircraft, maybe AA would still be viewed as the best Oneworld solution for the MAN-JFK market.
Wizz Air. This airline is gradually evolving from its earlier model of sticking to backwater airports. BHX is a recent beneficiary of this and it is not alone. It would therefore be worthwhile for MAN to make a pitch. If MAN can offer a pricing-structure acceptable to Ryanair then they can do so for any other ULCC.
A certain pink and purple airline is actually well aware of demand derived from the Manchester area. Some years ago I was puzzled to note advertising posters in Krakow (Poland) promoting their scheduled flights between Krakow and Manchester. However, the small-print revealed that the flights in question were actually Katowice-Liverpool! Giant porkie-pies at both ends of this claim! I guess that Poland didn't have an effective 'Advertising Standards Agency' at that time. However, somebody had certainly recognised where the underlying traffic demand actually lay!