Mongolian Spots: These are benign flat congenital melanocytic lesions that are common in infants, especially those with darker skin tones. They typically appear as blue or blue-black spots and are most often found on the lower back and buttocks but can also appear on the head. They usually fade by the age of 5.

Bruises: Given the age of the child, accidental trauma or handling could result in bruises, which might appear as blue or black spots.
Congenital Nevi: These are moles present at birth and can appear anywhere on the body, including the head. While they are generally benign, their appearance can vary, including being blue or black.
Café-au-Lait Spots: Although typically lighter in color, in some cases, especially in infants with darker skin tones, café-au-lait spots might appear more pronounced and could be considered in the differential for blue or black spots.

Child Abuse: It is crucial to consider non-accidental injury in any infant presenting with unexplained bruises or marks, as this could be a sign of physical abuse. The location, pattern, and age of the bruises, as well as the history provided, are critical in assessing this possibility.
Meningococcemia: Although rare, this condition, caused by Neisseria meningitidis, can present with a petechial or purpuric rash that might initially appear as blue or black spots. It is a medical emergency.

Blue Rubber Bleb Nevus Syndrome: A rare condition characterized by multiple venous malformations that can appear as blue spots.
Phakomatosis Pigmentovascularis: A rare condition that combines vascular and melanocytic nevi, potentially appearing as blue or black spots among other skin manifestations.