I'm just going to make a list of all the factors I can think of that affect stability, but please be aware that this list is not exhaustive.
- front tyre size/width
- front tyre weight
- front tyre pressure
- front wheel size
- front wheel rigidity
- headset angle
- trail
- front fork rigidity
- front fork travel
- front fork suspension friction
- front suspension travel shape
- front fork preload
- stem length / handgrip position relative to steering pivot
- handlebar rigity
- grip size and firmness
- primary frame/main triangle rigidity
- main triangle size and angles (affects BB to handlebar and seat position)
- rear triangle rigidity
- rear suspension type
- rear suspension travel
- rear suspension travel shape
- rear suspension preload
- slop in suspension pivots (all six axes)
- slip in all the other bearings - headset, bottom bracket, wheel axles etc
- BB to ground distance
- seat height
- seat front-back position
- seat firmness
- Q factor (BB/crank/pedal spacing)
- chainstay length
- rear wheel size
- rear wheel rigidity
- rear tyre size/width
- rear tyre weight
- rear tyre pressure
I am certain that I have missed some, and a few of the entries above should really be split out a great deal more - the rear triangle could be made of composite materials allowing fine, semi-independent control over rigidity in different axes, for example. And vertical compliance of the main triangle is a subject of intense discussion in some cycling circles. Likewise, suspension design is a complex subject that's quite different from suspension tuning, but I've largely conflated them in the list above.