Every single battery I looked up in a service manual had a different part number. Sony can't have made much money when everything they made was custom.
So long as any replacement is no wider and no longer, it should work, though the run time might lessened.
I found one that looks about right, but it may be too thick:
https://www.sparkfun.com/products/339
Or this one:
http://acrobotic.com/pwr-00009.html