FIR filter design for response inside unit circle
Note that an FIR filter's transfer function is completely determined by its behavior on the unit circle (or any other closed contour). So if you were to define a desired $\mathcal{Z}$-transform (instead of a desired frequency response on the unit circle), you could just evaluate this desired transfer function on the unit circle and use one of the many standard design procedures.

If it were convenient for you to specify a desired response on a circle in the $z$-plane with radius $r$, you could also just use a standard frequency domain design procedure, and obtain your final coefficients by computing

$$h[n]=r^{n}\tilde{h}[n]$$

where $\tilde{h}[n]$ are the coefficients obtained from the standard design procedure.

Of course you can also directly specify the desired zeros in the complex plane, as mentioned in Jason's comment. Note that you can't specify the poles because for a causal FIR filter they must lie in the origin of the $z$-plane.