There are two ways of dealing with this. The more general way is to state the solubility product. Taking your first example, this would have the same value no matter how much acetate is present in solution before adding the silver ions. The disadvantage is that for highly concentrated solution (in fact, in the presence of ions, even for moderate concentrations) this gets inaccurate unless you switch from concentrations to activities.
The other way is to specify the solubility of $\ce{AgNO3}$ (I switched to $\ce{AgNO3}$ because it is more soluble than $\ce{AgCl}$) in pure water, in 0.1 M sodium acetate, in 0.5 M sodium acetate and so on. Similarly for AgCN, you could specify its solubility in pure water, in aqueous solution buffered at pH 7, or buffered at any other pH. For the latter example, you should probably also specify ionic strength or the entire makeup of the solution prior to adding AgCN.