this generally requires doped paper/pulp or woven fabrics - anything to "deaden" the sound of the diaphragm itself and prevent ringing
I would add that the latest approach is to this problem is to use "Constrained Layer Damping" - instead of doping a speaker cone with a viscous damping fluid they are now sandwiching a viscous fluid between two rigid cones - kind of like a springing car suspension with "shock absorbers" to dampen it. This idea works well because the internal energy within the cone is lost as the constrained layer shears.
Basically if you can't dissipate the stored energy in a rigid cone you unavoidably end up with some resonance - after all this is exactly how cymbals are made and they ring a long long time...