They seem to come at random. Players try to predict them, but as far as I know it's mostly guessing.

However, it's been a while since the last etchings global discount, so that one might come soon. As for large coils, only if you get lucky on the Wheel, which is highly unlikely.

My wheel ain't broken anymore, but it's missing a few spokes. Same ole useless offers. Never had the large coil offer. Can't even get a prestige anymore. At least I'm saving valuable rubies.