It is compulsory for all listings to have either paypal or paymate or credit card payment option.

However, you put PICK UP ONLY for example in your title and in your description and you can list it for pick up only like this (from another poster)

The "proper" way to list is somewhat hidden, (that is, a seller generally has to see and click a link to open up a window for more options, then add the local pick-up only as an option, then save the option, then select it in the postage section - which removes all other postage options - and submit the listing that way. Only then will search results say "Free; local pick-up only).

Do not use COD - that means cash on delivery by Australia Post which is an expensive postage option.