it all depends on how much trade power you have.
i assume you can look around at potential trades on the II website...can you see any 2BRs? (what you can see is pretty limited - that will just be the leftovers after all requests have matched.)
if you are requesting a trade that is not currently available, you can limit the request to resorts that you know only has 2BR villas (such as marriott's sabal palms resort in orlando). if you have enough trade power and a unit becomes available, then you have matched for a 2BR. but if your trade doesn't have enough power, you'll never match.
(you can look in II's resort directory to see what resorts only have 2BR villas as an option - the marriott board here on TUG has a list of marriotts with only 2BRs that can sometimes be helpful.)
but to figure your trade power takes some time since II hides the numbers they are looking at - so you start by looking at the instant trades that are possible. then you can keep an eye on TUG's sightings board and compare what people see there with what you can see with your deposit (sometimes marriott or starwood preferences interfere, as only owners of those brands can see new deposits made by those brands of resorts.) but it's fun to learn and play with it (but it's good to keep in mind that even trades of 1BR for 1BR aren't that bad of a deal...)
