Thank you for all the responses. Looks like the best way is the search using "2" people. Then before booking, call the hotel to ask if a baby is allowed as the 3rd person.

Why this came up is that I was looking at the JW Marriott Essex House in Central Park New York. On the lowest level award room, it says "2" people max, cribs not allowed. Room comes with King bed on a 330 sq feet room, which makes me think that is odd since 330 is big enough for a crib. I am also thinking baby can sleep with us, not ideal but okay for a couple of nights. I got Marriott gold status due to match from United Airlines gold, but I don't know if I can count on it for a room upgrade to a room that fits 3 people.

Alternatively, I can stay at the Ritz Carlton Central Park (base room for 3 people), but with my point balance, I can do that for only one night rather than two nights.