The Silverback SRS is one of the best stock sniper rifles you can buy. I know. I know. Everyone is telling you that your stock gun is fine while not giving you very helpful upgrade ideas. I can do both. Stay with me.
One of the key skills of any effective airsoft player is knowing your weapon. Use it. Use it. USE IT. It should be second nature to you. You should know its kinks and idiosyncrasies. If is pulls one direction or another. How tight or loose is the trigger. Where is the trigger break? How far back do you pull the bolt? On and on and on. You should have some level of muscle memory. Know your weapon and know what you want to change before you change it. When you do, you will be able see/feel the difference between the stock performance and upgrade.
Let's assume that you are already familiar with your weapon and I'm just wasting your time by reminding you of the basics. One of the best upgrades you can make to any weapon is the barrel, but a sniper rifle makes a barrel upgrade a special task. You need something to tighten your groupings but also increase distance while at the same time maintaining silence. If you are a serious sniper, you know stealth is about both sight and sound. Your ghillie suit will only do you good if the other team can't tell where the shot is coming from. For that, I have opted for two upgrades. The barrel and the piston.
The barrel I use these days is the maple leaf crazy jet. It might seem like a gimic just by looking at it, but boy, does it work. I like to leave enough room from the end of the inner barrel to the end of the outer barrel so that I can "internalize" the silencer. Which means I got a shorter barrel than the one that came with it and packed the last few inches with dampening material. The outer barrel diameter is 20mm. So there's plenty of room.
The piston. There was really only one tried and true choice for a piston that was both efficient and silent and that was the WASP by snipermechanics. You just can't go wrong with this system. It will cost you, but it is worth it.
The only other upgrade can really only be classified as a modification, not an upgrade. I pack my frame with foam. There isn't a lot of dead air inside the frame but there is enough to leave you with an "echo" or ringing sound after a shot. By packing the frame with some lightweight material, you can eliminate that problem.
Good luck to you.