How to silence the AF on a Nikon D3100?

I have a Nikkor 18-55 VR lens and every time I take a video it keeps making this obnoxious sound and the microphone picks it up.No, I will not turn the continuous AF off.

Well then your only choice is to buy a separate microphone to mount onto the hotshoe, assuming it has a microphone jack. I have a camera that does the exact same thing, there's nothing you can do about it but attach a different microphone.

Either that or buy a USM lens (ultra sonic motor).

With that last comment you're actually answering you own question. You know what's causing the problem but you choose not to fix it.

You think the lens on your Nikon D3100 is noisey? When I bought my Sony SLT-A77 I didn't have a single lens with inbuilt AF, they all relied on the in camera AF motor! Screw-drive AF motors and in camera gears are REAL noisey! But one of the reasons at the time for my upgrade was VIDEO! So first off I bought a far quieter lens, but as the noise from the lens AF is transmitted through the body I quickly realised I had to add on a shotgun mic on a noise deadening mount.

Shot gun mics only pick up what is in front of their barrel, so you mount this in such a way that the tip of the mic barrel is level with or in front of the lens and you'll get almost no AF noise!