Silenced sniper rifle
There are a few steps involved to get a suppressor for the non-lethal sniper rifle.
First, you need to develop a sniper rifle with a suppressor. It does not matter which one, as long as it has a suppressor.
The next step is to unlock the legendary gunsmith. To do that, you need to finish 3 side-ops: 107, 108 and 109. This allows you to customize weapons in your ACC.
With a developed sniper suppressor and the legendary gunsmith, you can then customize your sniper rifle and attach the suppressor.
It is worth noting that only one side op appear per region of the map. So, you might be able to do 107 but 108 will not appear till you have completed the other side op(s) in the appropriate regions.
Once you rescue the legendaty gunsmith (Side Op 109), you will unlock the ability to customise weapons from the ACC menu. Suppressors can then be attached to guns from there.