This might sound a little odd, but it is quite an popular question it seems. This guide is the definitive source on how to install a peep sight on a compound bow string without using a bow press.
The answer is: DONT.
The main reason for not doing this is because the bow holds so much energy that if you try to tamper with it, you are almost certainly going to end up injuring yourself or someone else for that matter. The number one rule for archery is safety first, and this applies to shooting as well as maintenance.
The bow press is designed to do a specific job, so let it do that. If you really need it fitted then take it to an archery store who will do it for you, and in most cases this will be quite cheap - sometimes as little as $10.
Another reason not to do this yourself is that you cant calibrate if properly. If you own a compound bow then you are serious about your archery or hunting. Either way, trying to find some way for a peep sight to be installed on a compound bow string without a bow press is asking for trouble. If it is not attached properly you may find when the string tenses the peep leans either side - just 1mm can make a huge difference on wether you hit the target or not.
If you are serious about gettig the most out of your compound bow, a small investment will allow a professional to install the peep sight for you. If you dont have the money, then be sure to save up and consider it a worthy investment. After all, you may not be able to shoot if you end up losing an eye!

