Have not heard about vasopressin for pulmonary hypertension but we did use it for systemic hypotension in neonates. I have read 0.05-1.0 U/kg/hr in the literature but have experiences severe hyponatremia with one patient.
Our case was actually a 26 weeker born with severe PPHN (PPROM at 20 wweks) and treated with iNO at 20 ppm. Vasopressin was given by my colleague to keep the mean BP at 30 mm-Hg (a practice I did not agreed but I was not at the scene). So the intention was not to use it for PPHN.
We treated a lot of neonates with PPHN in our department in the last years. The major indication for vasopressin in these patients is systemic hypotension associated with PPHN or sepsis. There is a good case study by Acker et al in the Journal of Pediatrics from 2015. We start with a dose of 0.2 milliunits (=0.00002 U/kg/min) and increase to 2 mU/kg/min (=0.0002 U/kg/min). Rarely a dose up to 4 mU/kg/min is necessary to achieve a sufficient blood pressure. I would recommend to start with 0.6 mU/kg/min and increase or decrease the dose depending on BP. Major side effect is hyponatremia which occurs in the majority of patient but can be treated by continuous sodium infusion.
We have used vasopressin in the context of PPHN and hypotension and mostly in babies with CDH. We have noted hyponatremia. The doses we have used are 0.0004 to 0.005units/kg/min. Have to take care in the context of poor left ventricular contractility.