Dear Vickie,
As a pediatrician I can tell you that there is no way to predict as to when / if the child will grow dark. It would really depend on how much of the skin color the child has taken from either parent. The maximum change may happen within a few weeks to a couple of months, however tanning maybe more prominent even at a later age.
I am sure that at some point of time though the people are likley to notice that he has a mixed parentage. It would be preferable to break this news before it is 'accidentally' noticed by your father / MIL.
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regards
Dr. Gupta