options:
1. remove by hand, repeat until zoysia fills in
2. weed killer, repeat until zoysia fills in

I don't know where you live. but I question if zoysia is completely hardy there.

Might take a look at this info:
http://www.zoysias.com/adaptation/

And, better yet, phone your county's Extension Service office to ask if it will thrive for you
http://www.csrees.usda.gov/Extension/

Here is a link that might be useful: locate your County's Extension Service office

Zoysia is generally a pretty tough competitor with weeds. If the Zoysia is thinning and weeds are invading, you might check it for excessive thatch buildup.