[finalcutpro78]"Is there a way to run it into my mini DV cam and record it from a beta SP deck?" Yes (see below).
[finalcutpro78]"Would S-Video work?" Yes, again, great way to do it.
The "yes" is conditional to IF your camcorder HAS an "input" function.
Some do, many do not.
What brand and model do you have?
One way to check is to put the camcorder in "VTR" (playback) mode, but do NOT press "PLAY".
Connect your BSP's S-Video cable into the camcorder's S-Video output (yes, OUTPUT).
Play a BSP tape and see if the image pops up on your camcorder's LCD or viewfinder.
If so, connect the AUDIO from your BSP into the camcorder's audio outputs (yes, OUTPUTS).
If you are a broadcast pro, you can (or can FIND someone who can) get the proper cables and adapters to make that all work.
You're ready to make your dub by putting the camcorder into "Record" and playing the BSP.