It is sad that, for even the most fervent New Zealand sports fan, her name is likely to cause more confused looks than nods of recognition.
Some might recognise the last name, but even the "Nunneley Casket", awarded to the champion national women's tennis team, is a little obscure - certainly not anywhere near on a par with the likes of the Ranfurly Shield or the Plunket Shield or the Jameson Belt.
And, if you are thinking of popping to the library to check out the various books dedicated to her extraordinary career, you are unlikely to have much luck.
But this is a New Zealand sporting champion and pioneer thoroughly deserving of her place in the New Zealand Sports Hall of Fame.
Nunneley was probably our first great female sports star, and she is arguably still the best female tennis player this country has seen.
Much of the information about Nunneley's life and times has to be sourced from the Encyclopedia of New Zealand.
She was English-born (September 16, 1872), hailing from Leicestershire, and the daughter of John Nunneley, a wholesale grocer, and Kate Young.
The younger Kate (christened Kathleen) took to the genteel sport of tennis racquets from an early age, winning several events before she turned 15.
"In 1891 she won the Brighton handicap singles title and in 1893 recorded victories in tournaments at Liverpool, Leicester, Nottingham, Northampton and Wellingborough," the encyclopedia reports.
"Although she never competed in the All England championship, Nunneley defeated the reigning Wimbledon champion, Blanche Hillyard."
Tragedy struck the family when John Nunneley committed suicide in 1893. A year later, Kate Nunneley brought the family - Kathleen had three brothers and a sister - to New Zealand, arriving in Wellington on Kaikoura, on December 7.
Nunneley joined the Thorndon Lawn Tennis Club and in December 1895, she competed in the New Zealand Lawn Tennis Association tournament for the first time.
Beginning a long stretch of dominance, she would win both the women's singles and doubles titles.
Selected to represent New Zealand at the New South Wales championships in 1896, she "played with characteristic style to win both the ladies' championship and handicap singles titles".
Tennis had been around a while, but was still seen as a sport for toffs, for jolly good chaps called Arthur and Rupert, who enjoyed a spot of exercise after elevenses.
Women's tennis, especially in New Zealand at the time, was of a fairly low standard. But Nunneley raised the bar, and was a pioneer in the code.
"Possessed of a powerful forehand drive and a keenly competitive spirit, Kate Nunneley did much to improve the standard of women's tennis in New Zealand," according to the Encyclopedia of New Zealand.
"Despite being severely handicapped by the dress requirements of the day, she was an energetic competitor who enjoyed playing and practising regularly against men."
Nunneley's unbroken run in singles at the national championships stretched from 1895 to 1907, a record that has still not been matched.
She also won 10 national doubles titles and nine national mixed-doubles titles, twice with the great Anthony Wilding, and was a leading member of the New Zealand women's tennis team that made a triumphant tour of New South Wales in 1909.
Comparisons with Wilding are interesting. Where he became a superstar and multiple Wimbledon champion overseas, Nunneley stayed at home. Who knows what her legacy could have been, had she returned to England to play?
Eventually, towards the tail end of World War 1, Nunneley did visit Europe, but by then she had retired from top competition.
Tennis remained a passion. In a unique gesture, Nunneley donated all her gold medals to the New Zealand association, to be melted down and made into a trophy.
The spectacular Nunneley Casket was first presented in 1928 and subsequently awarded each year to the winning team in the interprovincial women's tennis competition.
Nunneley returned to England to watch Wimbledon in both 1949 and 1953.
Away from tennis, she was proudly independent.
"She never married and for 30 years she enjoyed a successful career as a librarian, retiring from her position as assistant in charge of the reference department at the Wellington Public Library in 1935.
"Known for her charm, modesty and good sportsmanship, she was a popular figure. For her own remarkable achievements and her enthusiastic work with young players, she was made a life member of the Wellington and New Zealand lawn tennis associations. She was also a life member of her Thorndon club."
Nunneley died in Wellington on September 28, 1956.
Kate Nunneley
Sport: Tennis.
Lived: 1872 to 1956.
Major achievement: Won 32 national titles.
