According to Apple's technical specification for that MacBook it can support up to 4GB. I looked at Crucial where I like to buy RAM and their search tool guided me to a DDR2 PC-5300 667MHz 4GB Kit. I have learned already that this search tool not always shows correctly, so I checked on System Profiler of the MacBook in question. The current 2GB RAM there was 2x 1GB DDR3 1067MHz. Exactly the same memory as I have in MacBook Pro 15-inch,  2.53GHz, Mid 2009, except I have there 8GB (2x 4GB). 

I've taken that 8GB out of MacBook Pro and put into the White MacBook. Works perfectly fine. So I have ordered for the White MacBook 8GB Kit (4GBx2) DDR3 PC3-8500, which works. 

Crucial should correct their search tool.