The risks associated with exposure to external fields of ionising radiation are important to quantify in order to provide guidance towards public and worker protection. In Publication 116 of 2010, the International Commission on Radiological Protection (ICRP) published adult male and female fluence-to-dose coefficients (henceforth referred to as dose coefficients) for external exposures to six types of idealised neutron fields. However, ICRP 116 dose coefficients are not appropriate for applications involving children due to their smaller body weight and stature. Our current work details dose coefficient calculations for children and young adolescents using the UF-NCI pediatric hybrid phantoms at all neutron energies considered in ICRP 116 (0.001 eV to 10 GeV); those dose coefficients with energy up to 150 MeV are discussed. The hybrid UF-NCI phantoms are divided into five separate age groups: newborn, 1, 5, 10, and 15 years. For these phantoms, we calculated dose coefficients for the six idealised neutron fields for 28 organs, two bone tissues, and the overall whole body effective dose. All calculations were performed using the MCNP6 radiation transport code. To validate our methodology, we first calculated dose coefficients for the ICRP adult male and female phantoms and confirmed our ability to reproduce the values published within ICRP 116. The same methodology was then applied to calculate dose coefficients for the UF-NCI pediatric phantoms. Energy-dependent trends were observed in the neutron dose coefficients for pediatric phantoms: below 100 keV, dose increases with phantom age (a proxy for body size); however, above 100 keV, the opposite trend was observed. Comparisons between field geometries showed varying trends depending on the location of the organ within the body. Explanations for these trends are also explored within. Our results are the first comprehensive set of neutron dose coefficients derived for children and young adolescents using the newest generation of hybrid phantoms. The primary application of the pediatric neutron dose coefficients presented in this work will be for a planned effort to update the dosimetry for the Japanese atomic bomb survivors.