Is it possible to determine a rotation speed (Vr) using other known V-Speeds? Is it possible to come up with a good estimate of rotation speed using other known V-Speeds? 

For example: if I know a plane has a Vs @ 55kt. and a Vy @ 75kt, is there a reasonable method to use to come up with a safe rotation speed?

This is a general question. I'm not looking for an exact rotation speed calculation (unless one actually exists, of course).
From FAR 23.51 that covers normal, utility, acrobatic, and commuter category airplanes:


  For multiengine landplanes, VR,
  must not be less than the greater of
  1.05 VMC; or 1.10 VS1


So 110% of the Vs of a particular configuration works. (Do not use for flight.)




Note from @Pondlife: 23.51 has been superseded with 23.2115 and the quoted definition is no longer there.
Related: What makes V1 one or two knots less than Vr on this performance table?