How can I stay with my Australian boyfriend? I am a UK Citizen.

NO!!! you are over 45 so not eligible for any visas or residency status...sorry

Under the migration laws, You do not qualify under the skilled migrate scheme due to your age but do qualify for a spouses visa if you have been in a relationship for at least one to two year before making the application, Note this depends on which State/Part of Australia you reside in, as each state have their own requirements. If you are not living together you must be able to show the following:

• knowledge of each other's personal circumstances; • financial aspects of the relationship, such as any joint ownership of real estate, joint bank accounts or other major assets; • the nature of the household including living arrangements such as joint residential receipts or joint household accounts; • the social aspects of the relationship, provided in statements (i.e. statutory declarations) by parents, family members, relatives, friends and other interested parties; • joint membership of organisations or joint participation in sporting, social or other activities; • joint travel.