Wanted Cheap air rifle

I am looking for a cheap air rifle preferably .22 not fussed about condition as long as it is in working order. Thanks

It is to help an elderly couple who frequently see at least two large rats in their rural garden, several poisons and traps have been tried with no success.
The next suggested option was for them to be shot preferably with a .22 air rifle to ensure their demise is quick and humane!
If there are any other recommendations on how best to deal with these vermin I am sure they will be happy to consider them.
Only trying to help not meaning to offend.