name the old time sailors cap that looked like a bedtime stocking cap

I found one single reference to the word "Liripipr". This may be what
you are looking for but I can't confirm it.

HAT GLOSSARY
http://www.villagehatshop.com/glossary_s.html

Regards;
tutuzdad-ga

Could this be it?

"There is considerable variety here, even among our relatively small
company. Many Glovers own what's called a 'liberty cap,' a kind of
stocking cap made of red or green wool, with a tail and tassel at the
end. These are warm in winter, though heavy for summer wear."

http://www.gloversregiment.org/Sailor.html

I Believe you may be looking for "Monmouth Cap "
 http://www.gtj.org.uk/item.php?lang=en&id=7998&t=1