My son spent half the year in California with his father, and half the year in Texas with me. I will be claiming him as a dependent on my 2009 taxes, however I was wondering if it is still possible for his father to claim the child care expenses he incurred in California to make up some of the cost?

Not possible. Only one of you can claim the child.

Actually, that is not technically true.

If the father is claiming Head of Household (possible if he provided a home for the child for MORE than half of the year), then he can claim child care expenses even if he does not claim the child as a dependent.