No, it's not at all difficult to find a context for "That won't be Tony". But it's much more likely to come after a suggestion that it is Tony.
A: There's the phone. That'll be Tony.
B: No, it won't be Tony. Tony said he definitely wouldn't be able to call before 9pm.
A: There's the phone. That'll be Tony.
B: No, it won't be Tony. Didn't you hear? Tony died in hospital last night.
I still say that "There's the phone. That won't be Tony" is not likely. Maybe:
A: Oh, I wish Tony would ring. I've been waiting for his call for a couple of days!
B: There's the phone now, but it won't be Tony. I'm expecting a call from Mary at 8pm., and it's just on that now. (Optional: Besides, Tony's dead, etc.)