Rubber bands work fine are are dirt cheap. Put an overhand knot near one end to make a second small loop - this is helpful to grab in order to get it back off the spool, or to loop over a tine of a treble hook to keep it in place tight to the spool when storing. While fishing, loop it over the tip-up frame and it will be right there + ready when your packing up.
I've also tried plastic tip-up spool keepers (from HT?). They work OK too, but they come in different sizes and some I ordered too small. Cost more than a band too! Good luck