A couple loses their only child and some time later they have another child. Is there a term for that second child? I once heard a parent use a phrase to describe it, but can't remember anymore.
I believe ‘rainbow baby’ is what you're looking for.
A rainbow baby is a term for a child born to a family that has previously lost a child due to miscarriage, stillbirth or death during infancy
Also according to Lexico:
A baby born subsequent to a miscarriage, stillbirth, or the death of an infant from natural causes.
A replacement child is a child conceived by parents to replace an older dead sibling.
This term originated in the field of psychology. Outside of the field, it should be used with care, as the death of a child is an especially sensitive subject, and the expression can be interpreted as an extremely callous thing to say.
In 1964 psychologists Albert C. Cain and Barbara S. Cain coined the expression:
Replacement child to refer to a child conceived shortly after the parents have lost another child.
In 1980, clinicians Robert Krell and Leslie Rabkin identified three types of replacement child: the "haunted" child, who lives in a family overwhelmed by guilt and silence, the "bound" child, who is incomparably precious and sometimes over-protected, and the "resurrected" child, who is treated as a reincarnation of the dead sibling.
Google Books shows that usage the expression “replacement child” has increased consistently from the ‘60s especially in medical, academic and specialized papers.
But the expression can be found also in more popular online papers such as:
I'm a replacement child - When Maria Lawson's older sister burned to death aged four, her mother was told by the family doctor to have another child. Which is how Maria came to be born, and – unbelievably – christened with the same name as her dead sibling
The Gift of Being A 'Replacement' Child - I grew up believing that I was a replacement child, for I was given life after another child lost his: a brother my family loved and missed, and whose absence cast an obvious shadow over my grieving mother's heart.
Usage note by @Laurel
“This term originated in the field of psychology. Outside of the field, it should be used with care, as the death of a child is an especially sensitive subject, and the expression can be interpreted as an extremely callous thing to say.”
@Lambie you are incorrect that it's what others say, because I myself am the proud mother of a sunshine baby, an angel baby as well as a rainbow baby and I say it about all 3 of my children. For the ones that don't know the meaning of these:
A sunshine baby is a child born before the loss of a child due to miscarriage, still birth or early infant death.
An angel baby is a child who gained their wings way too early, either still in the womb or in early infancy.
A rainbow baby is a child born after the loss of an angel baby.