Answer
$A = \frac{(M+m)~g~\mu_s}{k}$
Work Step by Step
We can find the maximum possible acceleration that could be provided by the force of static force on the block of mass $m$.
$ma = mg~\mu_s$
$a = g~\mu_s$
The maximum force exerted by the spring occurs when the spring is stretched or compressed to the amplitude $A$. Let $a = g~\mu_s$.
$F = (M+m)~a$
$kA = (M+m)~g~\mu_s$
$A = \frac{(M+m)~g~\mu_s}{k}$
