I think it rather depends on which B&S engine you have.....
If it's a newer type with a plastic carb mounted directly on the fuel tank (pulsa-prime?), then yes hunting might be a diaphragm problem. (I have "rescued" a diaphragm in the past by simply rubbing it with petroleum jelly - not sure why it worked, but it did.) But it's also worth checking there's nothing interfering with the governor linkages - perhaps do that first!
If it's an older model with a cast aluminium carb mounted on the fuel tank (pulsa-jet), the hunting won't be due to the diaphragm (which is merely part of the fuel lift pump), but could perhaps be a symptom of loss of compression..... or a binding governor linkage.... or a badly worn main jet screw (needle valve)..... or it could just be one of the mounting screws that hold the carburetor and fuel tank to the cylinder block has worked loose (first thing to check?).
If it's an older style unit with a bowl type carb (flo-jet?), then I haven't a clue
