A quick check of kayak.com revealed the following properties that meet all of your required criteria, listed by price in descending order, all are less than $140/night, including taxes:
The Palms
Rondel Village
Xtabi
Foote Prints
Sunset on the Cliffs
I did not list properties with more than 40 rooms, since you seem to want a smaller, quieter hotel experience. The following are in your budget but have more than 40 rooms, but less than 70...:
Rooms on the Beach
Legends
White Sands
Samsara
Travellers Beach
There are more properties with the beach or cliff location, but they do not have pools. I didn't bother to list these, as this seems to be a deal breaker.
There are also more properties that DO fit your bill, but aren't listed on sites that kayak.com searches, or don't have their Feb/March data available yet....
Catcha would be nice. I would have checked, but their website is down....
