You can freeze feijoas whole and unpeeled.
To do that, lay them out on trays in a single layer, ideally not touching and once solid you can bag them up, making sure to remove any air from the bag.
Sitting them standing up in egg trays makes it easier to avoid touching if your freezer is large enough.
Alternatively, you can also peel them then cut into pieces and freeze - but you do run the risk of the flesh going brown in the process. If you're going to cook them anyway into a chutney or similar this won't be a problem, but also I don't know that it will help you much.
Lastly, you can peel and cut them up then stew with white sugar (80 per cent feijoa to 20 per cent sugar) until just cooked before packing into freezer bags, removing any air, and allowing to cool. Then lay flat on trays -which will speed up the freezing process as the density is less -and freeze.
Generally we always cook feijoas with sugar - but if for some reason you'd like to avoid that, simply stew over a lowish heat with a little extra water and fresh lemon juice until gently boiling.
Cook for 5 minutes, stirring frequently, then bag up as described.
