In accordance to Tip #2, read your child some old Greek myths about the gods and heroes of Olympus as bedtime stories. Don't mention that they're real, but don't claim them to be fiction, either.

Also, I suggest avoiding putting you baby into boxes and/or fires to make them immortal. It won't work. Only the great deities themselves have the power to do that. (And I don't think you want to end up with charred baby).

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1) Be an avid reader - comment, vote, interact
2) Submit your own stories, tips, tricks, reminders, or others to me through PM (either from the POV of a demigod or their parent), and it will be published!