As explained in a tweet from Zapier themselves, the key to correctly saying 'Zapier' is to remember that it rhymes with 'happier'.
It doesn't seem quite right without two of the letter p - but hey, it's their name!
Still, when Wade Foster did an AMA on the Zapier Community forum, we made a point to ask.
To quote the answer:
We wanted API in the name since Zapier is built on APIs. We though Zaps were cool too. We found Zapier available for $9.99 and went for it. We couldn't afford Zappier.com at the time either.