Hydrocele: This condition is characterized by a collection of fluid around a testicle, leading to scrotal swelling. The positive illumination (transillumination) test, which shows a blue discoloration, is indicative of a hydrocele. It is a common condition in newborns and can be present at birth.

Inguinal Hernia: Although less likely given the positive transillumination test, an inguinal hernia could cause scrotal swelling. However, hernias typically do not transilluminate.
Testicular Torsion (early stages): While testicular torsion is an emergency, early stages might not present with the typical severe pain and could potentially be considered with a swollen scrotum. However, the absence of pain and the positive transillumination make this less likely.

Testicular Torsion: Despite its low likelihood based on the provided symptoms (lack of fussiness, positive transillumination), testicular torsion is a medical emergency that can lead to loss of the testicle if not promptly treated. It's crucial to consider this diagnosis in any case of acute scrotal swelling, even though the symptoms don't fully align.
Necrotizing Fasciitis or Other Severe Infections: Although rare and not directly suggested by the symptoms, any sign of severe infection (e.g., redness, warmth, swelling, and especially if accompanied by fever or irritability) must be considered due to the potential for rapid progression and severe outcomes.

Meconium Peritonitis: A rare condition that can cause scrotal swelling due to a meconium leak in utero, leading to an inflammatory response. This condition would likely be associated with other symptoms and findings.
Scrotal Edema due to Lymphatic or Venous Obstruction: Rare conditions that could potentially cause scrotal swelling, though these would be unusual in a 2-month-old without other signs of systemic disease or trauma.