We bought a memory foam mattress that came in a large box but definitely a size that would fit thru any door or stairway. The mattress was vacuum packed and instructions were to not sleep on it for 2 days. It took that long to return to it's proper size.

Ok, the vacuum pack takes care of the up. Now what about the down?? ;-)

Here is another option. It's a bed in a box, quilted foam with a built in coil base. I bought this in a full in June of last year and so far so good. It is a little firmer than I thought I would like but my back really likes it. It comes in a box and pops out to a mattress. Amazing!

Here is a link that might be useful: Sleep Master deluxe in a box Amazon

We bought a memory foam mattress from Costco because it was rated so high by Consumer Reports. We weren't sure we would like it and Costco has a super return policy. It came vacuum packed in a not too big box, but it weighed 130 pounds!

I think getting it down narrow stairs wouldn't be much of a challenge, as long as you don't mind having your walls scuffed slightly. It has no stiff internal pieces. I think it would just be a matter of squishing and pushing/pulling.

We have a king-sized latex foam mattress from SavvyRest, and it arrived in a bunch of boxes. The mattress is made up of six slabs of foam (three for each side of the bed), all zipped up into a cotton outer cover. We didn't need to take it apart when we moved, but it would have been easy to do so. It's a great option for narrow passageways!

We have two of those compressed ones. One apparently popped a leak in the vacuum packing in transit because it never arrived.

YOU MAY NEVER GET IT OUT OF THE ROOM - although they are flexible, they expand

IKEA also sells a California King mattress that is foam and comes rolled up. I have had it for five years or so and it is very comfortable. It is also very affordable. I had the issue in my 50's home where the attic was turned into the master suite.

We've had a pair of extra long twins used together as a king for 50 years. (Well, we've replaced the mattresses from time to time!) There is a foam insert "V" between the mattresses, and the mattress cover goes over that. This is also so much easier to handle when it's time to turn the mattresses.

We had one of the memory foam mattresses that magically expands. It was for the guest room which dh uses when his snoring gets too loud. Even after airing out before making the bed...the odor was so awful, dh couldn't sleep on it.

After two nights of trying, we sent it back.