These do brazilian for men or did in the past as my list is quite old so could change. these are mostly legit beauty salons and dont expect anything but a professional service.
Mankind Surry Hills
Face of Man CBD
Millk Medi Spa Darlinghurst - They have male and female waxers
The Beauty Bar Alexandria
Everywhere Beauty Cremorne and Lane Cove
Leah's wax works - Some stores do not do it
The Beauty Room Mosman
Anastida Makeup & Beauty
Ritz Skin Clinic Kogarah
Essential Beauty - It is a chain so some stores might not do it
Violet's Beauty Spot Carlingford
Elizabeth Skin Care & Electrolysis Balmain
Belle Journee Edgecliff
Madam Jenny Waterloo
Manwax Oatlands
Gloss Beauty Salon Prestons
Ouch waxing Studio Bonnet Bay
Pearl Nails Eastgate Bondi Junction. Other predominantly nail salons also do brazilian waxing

Beauty Wax Bar Bondi - extras may be available as the owner of the rnt took over
Epsom Beauty and Massage Rosebery - extras may be available here as they do rnt and you had to book as the waxer isnt always there

There seem to be now than there were several years ago.
Some beauty salons dont list it on their websites but do it. I have called up asking and have been told no, only to ask in store when i have been past to have them say yes.
Have noticed a few korean beauty salons also offering brazilians for men but can not remember the names
There are the rnt that offer waxing as well which have already been mentioned and also some salons that are run by males that i have not included.