you have to say it on the first day of any month which contains the letter R: White rabbits!

Similar things in the UK when I grew up, except that in my family we had to say 'Rabbits and Hares' rather than 'White Rabbits'. I think I knew both variations before I lived overseas, but I'd never heard the 'pinch and a punch' until I got to Oz. So maybe that's the one they should put on the word map?

In my understanding too, the words (whichever version you go with) have to be the very first ones you utter that month to be effective. (some kind of goodluck incantation?? - there's more to this than I realised when I started...)
All well and good if you a)remember what day of the month it is first thing in the morning when you wake up or b)don't ever indulge in the kind of latenight activity where midnight passes unheeded and you find you've said something else before you realise!

And this is the first time I've heard of the limitation to months which contain the letter R - I always thought it was all months. The letter R rule was for eating oysters or when to water cacti or something.