Oops, it doesn't look like 'engagment day' is a national day..

Other days

martini

Martini Day
book

Book Day
self appreciation

Self Appreciation Day
youth

Youth Day
fiancee

Fiancee Day
ponytail

Ponytail Day
girl friend

Girl Friend Day
buddy

Buddy Day
pampering

Pampering Day
boy friend

Boy Friend Day