I am trying to find out the name or type of old couch, divan, or sofa
that my parents owned in the sixties, the date of the couch may go
back further.  It was arm less and the seat folded up then down to
convert to a bed for sleeping. While in the upright positon there was
a storage area under the seat.  If I knew what it was called I could
do a search on either vintage or new retro styles

The name for this style in german is: Klappcouch
Hope it helps,

Ninchen

As a person who grew up in the '50s, I'll say that this sounds to me
like a davenport. Not all davenports were armless, but some were.

"A creation of the 1950s, the seat and back of a davenport can be
flattened into a sleeper, yet there won't be the gaping hole between
the mattress and the back of the couch that usually forms in a sleeper
sofa.

Absent are the metal or wooden slats used on futons, and the
davenport's padding is built onto the frame. Some even have built-in
storage under the base, where blankets, sheets and pillows can be
stored for optimum efficiency."

http://www.azcentral.com/home/design/articles/0828sleeper28.html