Zoysia grass (or Zoysiagrass) is a warm season grass. It has a very dense root system, and this makes it very difficult for weeds to germinate and grow.
Zoysia grass should be mowed short. Between 2 and 2.5″ tall. It also requires some water weekly. Ideally, you want to rely on rain water, but if irrigation is needed, 1″ of water per week should be more than enough. Occasionally you will have some weeds, that will be able to grow despite the dense layer of roots. There are several methods con control weeds on Zoysia.
Zoysia Grass Maintenance
This type of grass tolerates well hot and humid weather. It wants to be mowed short, and it does fairly well with moderate traffic. A healthy lawn will have an almost bright color, with straight an slight coarse blades.
One of the main things to be aware, is the possible buildup of thatch. Organically there is a very easy way to fix this problem. Compost and compost tea are the things that I would recommend. Compost brings texture and nutrients, and the tea will bring lots of beneficial microbes.
Fertilization is very simple. You can either apply fertilizer (liquid or granular) every 5-7 weeks. Do not bag the grass clippings, because they are a good source of nutrients for your grass. I firmly believe that if you have a healthy organic lawn, you can enjoy and play on the turf without the use of fertilizers.
Regarding weed killers, organically we are aiming to grow healthy turf. We will not use any kind of Weed and Feed because of the health risks of those products.
A product you could use is Corn Gluten Meal as pre-emergent for weeds. Some people get great results using it because they see fewer weeds every season. however, I am still not too sure about it. But I would rather try to change the soil pH, and use compost to make sure the soil conditions are ideal for Zoysia grass to grown. Weeds grow because the environment is ideal for them to grow, so instead of using pesticides, make sure to changing the soil conditions, so weeds will stop growing.
Feed the soil and not the grass. Avoid pesticides, and enjoy your lawn!