As a child, Maxi and Sam played the violin, and Madge played the piano. In addition to singing with the
Little Dublin Singers and
Young Dublin Singers, Maxi sang in the school choir at
St Louis High School, Rathmines. When
Eamonn Andrews wanted to create a
girl group to sing
backing vocals for his
recording studio, he chose Maxi,
Adele King, and
Barbara Dixon because of how the combined singing voices sounded; the girls became
Maxi, Dick and Twink based on all their respective
nicknames. Maxi credited this imposed friendship with drawing 14-year-old McCoubrey out of her
shyness. The group proved very popular outside Andrews' studio, and toured internationally (once to
Mainz with chaperone
Maeve Binchy). After seven years performing together, the group disbanded when they began developing conflicting goals. In 2015, Maxi told the
Irish Independent that the three "are still getting along today. [...] We're still friends, and chat and e-mail all the time." At 23 years old, Maxi was chosen to represent
Ireland at the
Eurovision Song Contest 1973, performing "
Do I Dream". At the competition in
Luxembourg, Maxi and the Irish delegation disagreed on the arrangement of the song. When Maxi refused to perform,
RTÉ panicked and sent
Tina Reynolds to compete in her stead, giving the replacement singer only the flight from Ireland to rehearse the song. Ultimately, Maxi performed and received tenth place. Reynolds would represent Ireland the following year with "
Cross Your Heart", placing seventh. In the late 1970s, Maxi applied to join the new girl group
Sheeba. Though she was initially turned down due to her age (28), she eventually joined
Marion Fossett and
Frances Campbell as the third member of "Ireland's first sexy girl group." At
Eurovision 1981, Sheeba came in fifth, singing "
Horoscopes". After traveling to
Holland and
London to record tracks for a new album, the three women of Sheeba were hospitalized at
Mayo University Hospital after a
traffic collision in
Castlebar; Maxi's
head injury caused
amnesia and needed more than 100
surgical sutures, Fossett received facial injuries, and Campbell had a
collapsed lung. Sheeba were dropped by their
record label after their recovery took too long, and though the three tried to succeed
independently, the group ultimately broke up. In 1985, Maxi joined the Irish
supergroup The Concerned to perform and record the
charity record "
Show Some Concern" in support of
Concern Worldwide; the song was a number-one hit in March and April 1985. The Concerned also included
Dave Fanning,
Pat Kenny,
Gerry Ryan,
Linda Martin,
Christy Moore,
Mary Black,
Adele King,
Maura O'Connell,
Freddie White,
Eamon Carr,
Johnny Duhan,
Dave King,
Clannad,
The Blades,
Stockton's Wing,
The Golden Horde, and
Those Nervous Animals. The
music video was filmed at
Windmill Lane Recording Studios. While she was bedridden in 2010–11, Maxi wrote 26 songs with
Charlie McGettigan; McGettigan later recorded two, while
Clara Rose Monahan recorded a third. ==Radio==