Well,.. I might try the commercial packing tape or just duct tape.

I have build a backyard rink for several years when kids were young but never used plastic, pack snow with snow shovel first and perhaps make level, build up sides with snow/slush, sprinkle water, layer by layer.

I've never used it, but I wonder if there's an extra sticky water proof Gorilla tape that could be applied to the plastic? Tuck Tape has a red colored construction grade Sheathing Tape that is strong and sticky. Today, I gave that tape a try by cutting a large Ziploc bag in half and then taping the two pieces back together and completely filling the bag with water ... leakage was minor. Would be ideal for you to have a large heated work place to lay the two pieces completely flat and overlap the edges and apply tape to both sides. A helping hand might make it an easier task to put down the tape without creasing it, as this is where the water will work its way out ... though, whatever minor leakage may occur would quickly freeze as you begin your base ice layer on a cold day.

we have built rinks the past 5 years... have tried taping a seem, but the problem was that it was too cold and the tape lifted - probably was -10. we were able to get a rink going, but bought a 1 piece liner this year and the time saving and the warm fingers was worth the cost - just fill er up and let it freeze. had the rink ready in probably 2-3 days instead nof weeks. of course if I had just the tarp I'd try taping. on a warm day with a cold night forecast to fill.