How long does the person intend living in the house? If any way medium to long-term, i think any form of heating by electricity is going to costs much more than heating by natural gas. The house sounds ideal for a combi gas boiler.
The first priority should be insulating the house to a high standard so that you need less heat in the first place.
All down to insulation and heat demand, but a kWh unit of heat generated by gas continues to be cheaper than the most efficient heat pumps, but if your heat demand is very low, the overall costs might converge to a point where the heat pump option makes sense.
The SEAI will not provide a grant for heat pump installation if you're not already around a B2 or better (with a Heat Loss Indicator of 2 Watts/Kelvin/m2) .
Night rates will apply during the hours of 1am and 8am in winter, but heat pumps need to run much of the day. A heat pump that will give you a COP of 3 during summer will likely only deliver ~2 in winter, assuming we're talking air-sourced.
We're talking about retro-fitting here, I'm not sure they're considering that level of disruption. Heat pumps need to run regularly throughout the day though, the lower output means slower cycle times. You could set a high target temp for the during the NR hours to ensure it's running throughout the cheaper period, but that's not advised as efficient.