Calculate transfer function of two parallel transfer functions in a feedback loop
Your two transfer functions are in parallel, i.e they simply add up. So your feedback transfer function is simply $G(z) = H_1(z)+H_2(z)$. You want to makes sure that the magnitude of $G(z)$ is smaller than one.

and the overall closed loop transfer function is

$$H(z) = \frac{Y(z)}{X(z)} = \frac{1}{1+H_1(z)+H_2(z)}$$