Hainan Airlines - I am sure BHX must be in talks with Chinese operators as they have so publicly stated that they want a Chinese route. Hainan now have the 787, a possibility for BHX in the future? They fly to TXL, BUD, ZRH and BRU in Europe right now.
Hainan have sadly dropped BUD-PEK; for me it always stood out as a bit of oddball route and after Malev suspended JFK and YYZ it was actually BUD's only long haul flight for a while - perhaps someone could fill me in. But I always thought that if they could make a route like that work then there could be hope for BHX bagging a Chinese carrier.
Given the presence of Star Alliance at BHX perhaps Air China could be a logical choice? I've no idea how there LGW flights are doing but as they are branching out from LHR perhaps there is potential here? Either way, the 787 is the plane for the job.
To be honest though I think getting Finnair with their connections to China would be great for BHX; along with TAP they are BHX's best chances of securing anymore Euro legacy carriers for the time being. And I know I've said it before but I still think Icelandair would be good for BHX as another option for the States.
And given Air Transat and all their upgrades/downgrades over the past few years perhaps Air Canada Rouge (Star Alliance again) is another one that should be on BHX's radar?