The Qld marriage fryerning found is defnitely the right one, given the Papua connection; see NLA Trove:
Cairns Post, Monday 15 October 1928
LATE MRS. S. SMITH.
The funeral of the late Mrs. Eva Mary Smith, wife of Mr. S. Smith, Customs, Fort Moresby, took place on Wednesday afternoon, moving from St. Monica's Church, and was attended by a large circle of friends. Rev. Father McFadden held a service at thc church, and also conducted the last sad rites at the Martyn-street cemetery. The floral tributes were from: Loving Husband and Son; ; Loving Father, Mother, Brothers and Sisters ; Loving Sister, Brother and children (Mr. and Mrs. J. T. Guilfoy); Loving Sister, Brother and children (Mr. aud Mrs. J. E. Baker, Gordonvale); Mrs, Corsar; Mrs. Jacobs; Mr. and Mrs. J. Molloy; Jack, Bertha, Fred, May and Esliensen family; Mrs. Millar and Mrs. M. Ryan; Mrs. E. G. Fox and family (Gordonvale); Mr. and Mrs. W. Houston and family.
Cairns Post, Wednesday 9 October 1929
SMITH.-In loving memory of my dear wife who died the 9th October, 1928. (Inserted by her loving husband, S. Smith, Papua.)
SMITH.-In loving memory of our dear daughter, Eva May Smith, who departed this life, October 9th, 1928
"May she rest in Peace."
(Inserted by Mr. and Mrs. S. Vale.)
So Sidney/Sydney Stephen SMITH was named after his father Sidney/Sydney SMITH and his grandfather Stephen VALE. Stephen VALE died in 1939, son of Wm & Mary (nee ROACH). He is also buried at the Marytn St Cemetery in Cairns (online database available). His wife Ellen died in 1956, daughter of Joseph MILEY & Ellen BYRNE.