Okay, for the first wedding ring I chose Tsubaki, the stumbling is something called Flower Tourmaline, already got other material by going to other areas.
During the events about marrying, Enaris brings you to a special dungeon below the church of Aldlyn, where you can craft the wedding rings. In the north of the dungeon are sparkling stones, which you can mine to get materials, including the special jewels for the wedding rings. These jewels can't be obtained anywhere else.
You need to have the mithril pickaxe to mine, and you need to upgrade it on the crafting table in that dungeon to be able to mine the better mining spots. The jewels like Flower Tourmaline can only be obtained from the spots you can mine with an upgraded mithril pickaxe.