Red Envelops can rarely drop the Gilded Invitation. However, he's an NPC that doesn't move in, and instead stays during the day and leaves at night, like the Traveling Merchant.

But, from what I remember he commonly arrives, to the point he can arrive several days in a row. His only function is you pay him a hefty fee for a possible Pozi Scheme and he gives you an effect that increases you're Luck for 30 Minutes.

So, just farm enough Red Envelops and i'm sure you'll get it at some point.