Zoysia is a warm season grass compared to our traditional cool season grasses. It is late to show up and first to go dormant in N. Illinois. In any kind of bed where you can selectively make a treatment, a non selective translocatable herbicide could be used. This should be absorbed throughout the plant and root system controlling the grass. if limited in scope, digging it out will also work. A simple non slective weed control product could also work, but a repeat application my be needed.
As both Zoysia and our preferred lawn grasses are both monocots, I am not aware of a selective material that will control Zoysia without harming your desirable grasses the above suggested herbicides will work,just taking out your good grasses too, so any treatments should be spot treatments only.
