Al Hill is 100% correct. At one time, Sony had a list of supported CPUs, but it appears that it has washed its hands of the product. You only have one option. Surf for all mentions of your laptop. Note which CPU is included. Any CPU you find is guaranteed to be supported. Also, you might find a list of the CPUs sold with that laptop. But heed Al Hill's comment that the BIOS must support it. It is entirely possible that Sony released your laptop and then modified the BIOS to support newer CPUs. Normally one does not modify the BIOS unless a specific problem is being solved, but in your case you probably should update the BIOS to the most current one before switching CPUs.
By the way, I was talking about surfing for mentions of your laptop on Amazon, Newegg, and other outlets which might have previously sold it. I did this for an HP laptop to find the list of CPUs which were supported. The process is ugly and time-consuming, but if Sony won't help you, it might be your only option.
As Al_Hill stated it is Sony's* product and he provided the list of the processors' family which is compatible with your laptop's socket.
Additionally, paramountain's idea is a good option, by checking Amazon*, Newegg*, BestBuy.com* and other* retailers you will be able to confirm specifications of the laptops they sold, this could give you a picture of which CPU's are compatible and already tested to be compatible with your laptop.
*Other names and brands may be claimed as the property of others.