It depends in what the nanoparticles are incorporated (suspension, or in a material?) but the killing effect depends on either silver ions or, if small enough, direct incorporation of nanoparticles into the bacteria. Generally speaking, they do not diffuse through agar like antibiotics so a disc diffusion method would not be suitable. If in an aqueous suspension, you could use a simple doubling dilution method, but the method of test needs to be linked to the intended application: are you intending them to work in suspension, or when incorporated into a (bio)material?