There are plenty of heating systems on the market, and one of them is bound to be ideal for you. It is worth finding out about some of the more unusual systems, like heat electric radiant ceiling systems.
Radiant heat of whatever design has several home use advantages that are often quoted. For example radiated heat does not move so much air around the rooms - this is good for allergy sufferers since the moving air is the perfect transport system for those allergens that set them suffering.
It is also true that radiant electric heat can be set at a lower thermostat temperature than hot air systems - it feels warmer, probably because it is a more even heat.
Systems that use water like hydronic radiant floor heat share these advantages too. But they need a furnace. With electric systems there are no flues or to outlets.
In fact installing the system in the ceiling space also means that there are no hot surfaces for kids to injure themselves on.
Ceiling radiator panels are usually flexible strips with heating wires running through them. They have to be installed by a professional, but they are quick and easy to do. This can make them a really attractive option that does not mean much upheaval at home.