Not looking to migrate permanently, but wanting to stay in Australia a little longer with child/children than what a visitor visa will allow?

The Sponsored Parent visa may be an appropriate option for you.

Unlike the permanent parent visa pathways, you do not need to meet the Family Balance test for this option.

To be eligible, you need to have child who is an Australian citizen, permanent resident or eligible New Zealand Citizen. They will also be required to apply for and be approved as a family sponsor. Once the sponsorship is approved, you can then apply for the Sponsored Parent visa.

You need outside Australia at time you apply for the visa, unless you have been given permission to apply whilst you are in Australia. You can choose to apply for a visa that is either 3 or 5 years in duration. Once granted, it will allow you to unlimited travel whilst the visa is in effect.  You will not be able to extend the validity period of this visa, however it can be applied again once you depart Australia. The total period you can be granted on the 870 visas combined, is 10 years.

It is important to note that this visa does not permit you to work and does not serve as a pathway to obtain permanent residency. While holding or applying for this visa, you are not able to apply for either a permanent or temporary parent visa.