Collocations for birth - noun

live
Better living conditions mean more live births and fewer stillbirths.

normal
difficult
breech
Caesarean, vaginal
natural (= without the use of drugs)
premature, preterm
multiple
illegitimate, out-of-wedlock (AmE)
home, hospital
water (= in water)

give
She gave birth to a baby boy.

register
celebrate
They recently celebrated the birth of their second daughter.

await
He was anxiously awaiting the birth of his child.

announce
attend
A doctor and three midwives attended the birth.

certificate
records
date
place (usually birthplace)
weight (usually birthweight)
process
complications
defect
canal
the mother's birth canal

mother
attendant (= person who assists a woman giving birth)
partner (= person a woman chooses to be with when giving birth)
plan
You should prepare a birth plan with your obstetrician.

announcement
rate
a low/high birth rate

at birth
The baby weighed seven pounds at birth.

at a/the birth, during a/the birth
The child's father was present at the birth.

by birth
He was American by birth, but lived in France.

births, deaths and marriages (AmE), births, marriages and deaths
announcements of births, marriages and deaths

your date of birth, your place of birth
of low birth, of noble birth (both old-fashioned)
the moment of birth