Availability can be found online, but I don't think the "search for availability" function really works very well. So your best bet to find availability is probably to call in.

BTW, in general, the best time to find availability for an MVCI property is when it is first opening up. There aren't as many owners yet using their weeks. Once a property is sold out, the owner has to sell back the property to Marriott before they can offer it with points. And I would guess that most of those are offered back for paid stays rather than for point offerings.