The hard part is that you really just want to use one of the two cables inside the s-video cable. S-video has two 75ohm cables inside of it (if it is good), and you only need one 75ohm cable with composite video. So, basically you need an adapter that allows you to just use composite video from source (your DVD/VCR) to destination (the projector).
Since you have no HDMI run in place, and no other cabling, the adapters I linked to should work okay. If they don't, then you may need to start soldering and hit up Radio Shack to buy some S-video ends, which you can solder a RCA end onto with a bit of cable between. It's not going to be pretty, but it will allow for a direct composite video path.
The adapters I linked above MAY do the trick though. The key is you want to use them at BOTH ends so you are coming out of the DVD/VCR composite, not s-video. You aren't trying to change s-video down to composite, that would, and should, use an active s-video to composite adapter. Instead, you are just trying to use half of the S-video cable as a composite only cable.
Oh - active adapter I say?
Yup... This is the real deal: http://www.ebay.com/sch/i.html?_odkw=extron+s-video&_osacat=0&_from=R40&_trksid=p2045573.m570.l1313.TR0.TRC0.Xextron+ycv&_nkw=extron+ycv&_sacat=0
The Extron unit is a pro-grade s-video to composite video adapter. It needs power, and does a great job. Not as cheap as the adapters, but yes, it works.