A family meeting was called with CYF staff, where it was agreed baby Eli would be declared in need of care and protection.
The baby would be allowed to stay with his mother, provided she could give him a home free of alcohol and domestic abuse, until both could be housed at a residential drug and alcohol rehabilitation programme.
Eli was born weighing 2.65kg on October 9, 2010.
He had some breathing difficulties, was small for his age and was slow to cry.
Eli very quickly became more active and was discharged into his mother's care.
CYF staff regularly visited and found his mother appeared to be complying with the discharge plan and was abstaining from alcohol.
By six weeks, baby Eli had shown excellent catch-up growth and weighed 4.9kg.
A post-mortem report found he appeared to be in a safe sleeping position when he died on November 20.
But there were two important sudden death risk factors - his growth was retarded at birth, and his mother had a history of alcohol use in pregnancy.
Coroner Smith has found both Eli and his mother received the best support and medical services available to them.
Eli's mother appeared to be following her support plan and was attending to her baby with care.
"There is no criticism of any parties and this was a tragic death."
Coroner Smith found Eli died naturally from sudden unexplained death.