We don't have synonyms for birth-day yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are birth, mirth and girth.
(n) :
(uncountable) The process of childbearing; the beginning of life; the emergence of a human baby or other viviparous animal offspring from the mother's body into the environment.
(n) :
(countable) An instance of childbirth.
(v) :
(transitive) To bear or give birth to (a child).
(n) :
(countable) A beginning or start; a point of origin.
(n) :
(uncountable) The circumstances of one's background, ancestry, or upbringing.
(adj) :
A familial relationship established by childbirth.
(n) :
(uncountable) The process of childbearing; the beginning of life; the emergence of a human baby or other viviparous animal offspring from the mother's body into the environment.
(n) :
(countable) An instance of childbirth.
(v) :
(transitive) To bear or give birth to (a child).
(n) :
(countable) A beginning or start; a point of origin.
(n) :
(uncountable) The circumstances of one's background, ancestry, or upbringing.
(adj) :
A familial relationship established by childbirth.