What do airliner manufacturers do with aircraft for which have no buyers?
New airliners without a buyer will be handled on a case-by-case basis. Of course manufacturers prefer to not be in such a situation, and there is no standard system for handling this. However, there are some typical ways that this is handled.

One option it to store the aircraft at the manufacturing site. This is the same (and pretty much only) option that is used for aircraft without engines. This has the advantage of being easier to work in and deliver, but will of course take up valuable space.

To save space at the factory, the aircraft can be moved somewhere else. Storage areas already exist primarily for older aircraft being stored or scrapped, but new aircraft can go there as well. Boeing has done this with some 747-8 aircraft, as well as C-17's.

Of course the manufacturer has spent money assembling the aircraft, and it is costing money to have it sit somewhere, so they will be eager to cut their loss as much as possible. These aircraft will probably be offered at a significant discount compared to placing a new order. However, buyers may prefer to wait and receive an aircraft straight from the factory, rather than one that has been sitting in storage for a while. There may also be issues with customized options applied for an original buyer that would need to be refurbished or accepted by a new buyer. Looking for new buyers and rearranging deliveries is not unheard of and is part of the business of making aircraft.

It may be that no one is willing to buy an aircraft, or the aircraft would otherwise not be economical to put in service. The aircraft may in this case be sent to a museum, as with the RJX. In a similar case, the first three 787 aircraft were not deemed economical to put into commercial service after the test program, and were sent to museums.

The last resort would be to scrap the aircraft. This is certainly disappointing for a new aircraft, but in some cases it is the only option left to regain any value.