Rings aren't
purely Christian - Christians adopted the ring, basically, not the other way around. The ring has simply been a symbol of eternity, and in many books, they're made in such a way to indicate lack of an end (Bringing a touch of irony in JRR Tolkien's novel). Removing the wedding/engagement ring on the grounds of it being
related to religion is somewhat excessive. Dwarves can like crosses in the game; I don't see why they can't use rings as a sign of betrothal or fidelity that has no end.
That being said, I think this is an excellent idea. If we're looking for something a little more 'Dwarf-like', though, try the Finger Armor Ring for some variety. Engravings on the ring will complete the picture - The name of the Dwarf's beloved would be inscribed on the inside, for example.
If we wanted to go more along with the spirit of Dwarf Fortress, though, Chairs, Floodgates, and a Silk Shoe would be considered perfectly acceptable wedding gifts - There'd just have to be some way for the owner to wear the item or for the player to be able to put it in that dwarf's room (Or somewhere the dwarf frequents - You want them to see it for happy thoughts, for example). If one in the couple or if both dwarves don't like a particular unperishable item, then they could use the traditional ring.
Marriage could also be expanded upon - The spouse should be considered a 'friend' and should attend parties with his or her partner accordingly.