In the last few years in south Africa the law regarding Air rifles has changed , and they are no longer required to be licenced,
so long as they are under .22 calibre and ( I maybe wrong here ) under 9 foot pounds of muzzle energy.
so a nice powerful .177 calibre rifle is well within the reach of most people.
While this isn’t much good at protecting a household from anything , its a very effective weapon to hunt small animals and birds, and while it is illegal to hunt with an airgun, in South Africa, if the SHTF , they could be used to take pigeons, and other birds, rabbits, cats, and other smaller animals or scare off dogs, and other predators.
Personally I would recommend a, spring or air ram, rifle that can shoot at about 1000 feet per second, and not a PCP or gas rifle, obviously cause they need gas to run.
The pellets are unrestricted and you can keep 1000’s of pellets and they are relatively cheap.
They are pretty quiet to shoot, and this is a tactical advantage if you are close to other people and don’t what them to know you are there.
a good scope is a great investment, and will improve your aim. Get one !
a sling is also important and lacking on most air rifles. get one and find a way to fit it.
I would also recommend LOADS of practice, Spring rifles have some recoil and you need to learn to roll with it 😉
I have shot maybe 10 000 pellets in my life and I can attribute my accuracy with a proper rifle to a childhood spent in the plots, doing target practice, for +/- 4 hours every Saturday morning for about 15 years, but to be fair the was with open sights.
Air rifles can be diesel’ed by adding a drop of oil behind the pellet, the pressure causes the oil to detonate and the velocity of the pellet is greatly increased, this can be bad for your gun , but does mean you get more power and if done seldomly and conservatively can push a pellet up to the power of a .22 LR , which may be needed from time to time, its an option, but a risk.
the scenario I would propose that an air rifle would be useful would be to “bug in” in a suburban environment, and have run out of food, you can take a bird or two, for the pot.