I've never dealt with Sony's support 'site but generally you'd look up specs on models in the same family, comparing case styling and hopefully find some pictures on ebay to compare bare boards. No quick and easy answer unless Sony support or a laptop repair shop can tell you. If they have a parts finder service you might also search it for the part numbers of some of the major components (besides the standardized ones, not optical, hard drive, memory for example) in case they list multiple models that part fits, then research those other models.
May we ask why you don't want to use an exact replacement?