I have a smallholding and have lots of rats.
I agree with not using poison. It is dangerous to pets and other animals.
In order to be humane sticky boards need to be regularly checked and you have to have a strategy to despatch said rat.
Spring traps are effective but need to be placed in a tunnel/box so pets and wild birds are safe from them. I find peanut butter to be the most effective bait.
An air rifle and some time is by far the most effective and humane way IMO.