Certified GKH Gardening Expert
Your best bet would be to hand pull as much as you can and then add mulch to keep weed growth to a minimum. However, you could also try sprinkling corn meal in the area, which has a chemical in it that acts as a pre-emergent on plant seeds preventing them from germinating. Sprinkling corn meal will not harm plants but will keep weeds from growing.
Another option (though not one I enjoy recommending) is the use of conventional weed killers. Here is an article that you may find helpful: https://www.gardeningknowhow.com/plant-problems/weeds/conventional-weed-killers.htm
Ortho Grass-B-Gon will kill weeds but won't harm your monkey grass.