Child born outside US to a US resident alien in the month of June 08, and later came to US to live in with the father in 2008. Child's age as on 31st Dec 2008 is 6 months, and lived in US with the parents in US for 2 months. Can the child be claimed as dependent? Is the child eligible for CTC and EIC?

Here are the rules for "Qualifying Child"

A “Qualifying Child”

Is the child U.S. citizen? Then get SS number and claim the child.
Even if the child is not a U.S. citizen, if the child lived with the mother and you are filing joint return, then you can claim the child. Attach W7 (ITIN application) with your tax return. Make sure to attach page showing child's entry to the U.S.
A dependent can be your qualifying child or qualifying relative. There is no age limit for a qualifying relative. For the requirements to claim a dependent (as your qualifying child or relative), read: Your U.S. Tax Return: Requirements for claiming a dependent

The child cannot be a citizen since neither of the parents were citizens and the child was born abroad.

For those unfamiliar with the requirements of the acquisition of US citizenship for a child born abroad see:

Acquisition of U.S. Citizenship by a Child Born Abroad

And further guidance at:
Documentation of U.S. Citizens Born Abroad

Neither the child nor the parents are citizens. If a parent is a citizens, this question would not have been raised. Both the parents are resident aliens by virtue of SPT 2008 and child is born outside US in June 2008 and brought to US only in the month of October. Your answers are answering my point.

The child simply cannot be taken as a dependent whether as a qualifying child or qualifying relative.

The child fails the citizen or residency test. See;
Tax Topics - Topic 354 Dependents