This is the best possible CPU I could find that *MIGHT* work on that laptop. http://ark.intel.com/products/40479/Intel-Core2-Duo-Processor-T6400-(2M-Cache-2_00-GHz-800-MHz-FSB)
Be sure to update the laptop's BIOS first and foremost to the most current! After that, you can probably follow this guide to get to the CPU to replace it: http://linuxtweaking.blogspot.com/2010/07/how-to-open-samsung-r510-notebook.html
I do not take responsibility should the processor fail to work. My findings are based on the fact that the laptop has had that processor available in variations of the same model. Its been said in the posts above that some r510s have the CPU soldered onto the mainboard, making replacement impossible. You do this at your own risk.