I am a self funded retiree. My entire income is from shares.I used to have a credit card with ANZ, but cancelled that as the upper age limit on travel insurance was 80.
I found Bankwest had a card with no upper age limit. They needed to see copies of every dividend statement of every company I held for the last 2 years in order to get approval to issue their no-fee platinum credit card.
That is a useful card to old people as it has no upper age limit on the included comprehensive travel insurance, as well as the fee free aspect. That could far outweigh any reward points scheme.
In all, the approval process took about a week as an overnight bag of paper copies of dividend statements was dropped into the Adelaide office and sent to Perth for them to rummage through.
Because my income was derived from shares they reduced that income by a certain percentage, to arrive at the credit limit on the card. They have a chart to show how different sources of income affect credit limit if you ask.
My tax office income statements weren't proof enough.
I think most banks would assume a credit card applicant is working full time. Proving an income stream could pose challenges to retirees.