Luckily, a friend of mine has a cousin called Nienke! This is what she gave me:
"
Can you believe it, my real names are
Trijntje Bootsma (my Frisian
grandmother's first name and maiden name). But according to my Frisian
father the nickname (noemnaam) for
Trijntje is Nienke - not sure why, but I know another Frisian Nienke who's real name is also
Trijntje. I think it is quite possible that
Trijntje comes from
Catharina and then became Nienke."
So, there we have it! She's right about
Trijntje coming from
Catharina - it would be pronounced more-or-less like train-ke - and, I think, confirms my suspicion.
All the best