How is the stability of a coordination compound in solution decided? How is the dissociation constant of a complex defined?

Stability of the compounds is defined as the measure of the resistance to replacement of the metal ligands with other ligands. Stability of the complex can be decided by the equilibrium constant of the dissociation equilibrium.
For example , for the reaction,
$C{u}^{+2} + 4N{H}_3$⇌ [Cu(NH₃)₄]²⁺
The equilibrium constant for this association reaction is equal to the stability constant of the reaction.
Association constant =  Stability constant , $\beta$ = $\frac{\left[Cu\right(N{H}_3{)}_4{]}^{+2}}{\left[C{u}^{+2}\right][N{H}_3{]}^4}$
The value of the stability constant is the measure for the stability of the complexes.
Dissociation constant is defined as the equilibrium constant for the dissociation reaction of the complex into ions. It is reverse of the association reaction. The dissociation reaction for the above reaction ,
   $\left[Cu\right(N{H}_3{)}_4{]}^{+2}$⇌ Cu²⁺ + 4NH₃
And its dissociation constant ,  K_d = $\frac{\left[C{u}^{+2}\right][N{H}_3{]}^4}{\left[Cu\right(N{H}_3{)}_4{]}^{+2}}$