There's at least two references on Pottermore to (professional) international teams having coaches.
The first relates to an article supposedly written by Ginny Weasley for the Daily Prophet
"Heartbroken Norwegian coach Oddvar Spillum had no comment for
reporters, but broken sobs. There can be no doubt that this has been a
deeply unlucky tournament for the usually outstanding Norwegians.
However irrational it may seem, many fans blame the Selma, a Norwegian
lake monster that the team brought as a mascot and which caused a
bloodbath at the opening ceremony. The Selma is tonight hiding in a
And the second is in much the same vein;
Snuka has previously been
dubbed an egoist by teammates and today’s actions will do little to
change his reputation.
Fijian manager and trainer Hector Bolobolo’s only comment after the
match was ‘I’m going to kill him'.
There's also a glancing reference by JKR in the new "History of the Quidditch World Cup" to the fact that dragons are not allowed on the quidditch stadium in any capacity, including acting as team coach.
The rulebook concerning both on- and off-pitch magic is alleged to
stretch to nineteen volumes and to include such rules as ‘no dragon is
to be introduced into the stadium for any purpose including, but not
limited to, team mascot, coach or cup warmer’