After his father died when Monaghan was four years old, Monaghan's mother had difficulties raising him alone, and at age six, in 1943, Monaghan and his younger brother ended up in an orphanage until their mother collected them again in 1949.
Setelah ayah Monaghan meninggal dunia ketika ia berusia empat tahun, ibunya mengalami sejumlah kesulitan dalam membesarkan dirinya, dan pada tahun 1943, saat ia berusia enam tahun, Monaghan dan adik laki-lakinya dimasukkan ke suatu panti asuhan hingga sang ibu mengambil mereka kembali pada tahun 1949.