Yes, you can put a piano on its side.  It is done by professional
movers when necessary, and that is often.

For spinets, be careful of breaking off the legs.  It is easier if you
use a piano dolly.  If you don't have a platform dolly, carry it to the
elevator with two to four persons.  Put a folded blanket under the end
you will be tilting and tilt onto one or two more folded blankets in
the elevator.  When you put it on its side, you have to watch out for
the music rack, and the top and key cover (if any) flopping open.

If you have never moved a piano use common sense.  Lift the piano up
to its balance point and let it down again.  Lift it up and over the
balance point to two people on the other side.  Practice until you feel
sure about what you are doing.

If it is a "Betsy Ross" that has come unglued, you might notice this
if the sides fall off, but this is rare unless it has been in a flood.
It is the legs on a spinet that are most likely to break during a move.

The greatest risk of putting a piano on its side is that stuff that may
have fallen in, like pencils, paper clips, bobby pins, coins, Christmas
cards etc, that can fall into new positions and cause blockage after
the piano is set upright again.

Richard Moody
http://www.pnotec.com/