Hey there!
Whether the Wedding Rings will be available to you for purchase on your next "Sex Shop Refresh" is nothing more than a roll of the pseudo-random number dice, for lack of a better phrase...lol
Just like everything else in BBE where there is a "chance for something to occur," the only way to "increase" the chances for it to spawn in your favor would be to have a nice size bag of diamonds in one pocket and your lucky rabbits foot in the other because even if you are lucky enough for it to show on the first attempt, you're still going to need 99 diamonds to actually purchase it from the shopkeeper.
(quick side story)...
There are actually custom titles that sell for 399 diamonds that appear even less often than the wedding rings do. In one full year of game play across two different servers, I have seen a custom title appear in the shop only one time and in 15 months just playing on UK2 server, i have seen wedding rings appear twice...and of course the second time I was low on gems and was unable to refresh the shop for three days because I really wanted them. The nice thing though, is after you marry someone on BBE you will find in your inventory, a silver ring engraved with your spouses name that you can equip like normal gear.
(circling back to the point)...
So yeah, just like when you're determined to get that stupid Epic Smelling Salt refinement for your shiny new boots and end up blowing 2000 gems...or my weakness, splurging on extra refreshes to complete an clothing set and even those frustrating times when you just HAVE to beat that one person in a duel that keeps defeating you with 1 hit point on their bar every time...every time you click that "go again" button when you are seeking a specific item or whatever, you're at the mercy of a random number generator that has been programmed extremely well and not in our favor.
Honestly, it sounds like total BS, but when I stopped thinking about it altogether...that's is when it came back around lol
Anyway, I wish you favorable RNG! (That's good luck in nerd)
--Emmy