I remember them by first knowing that the charges count down from left to right and the number of oxygens remains the same for that period. So I remember the first polyatomic from each period being CO3
2- and PO4
3- as "2,3,3,4". 2,3 meaning a charge of 2- and 3 oxygens for a carbonate ion and 3- charge with 4 oxygens for phosphate. Then you simply count down the charges from left to right, keeping the oxygens the same.
CO3
2- NO3
1- PO4
3- SO4
2- ClO4
-The exception being chlorate which is actually per-chlorate following that progressive pattern. Chlorate would be ClO3
-. Hope that helps, it works out alot faster in my head when I'm doing calculations.