If you're determined to try it with just the console in 'Skyrim', here's what I've learned from tinkering and breaking a few save files along the way.
First, make a manual save. I can't stress that enough — messing with factions and relationship ranks can produce weird behavior. Open the console (~), click Serana so her reference ID shows at the top, then type: addfac 19809 1. That adds her to the marriage faction. Right after that, with her still selected, type: setrelationshiprank player 4 which gives her a high relationship rank with you. Exit the console and try interacting normally.
Real talk: Serana is scripted in 'Dawnguard' and doesn't have normal marriage dialogue wired up. Those two commands will make her eligible in the game's faction system, but you probably won't get the standard marriage ceremony or the Amulet of Mara dialog. If you want a clean, fully functional marriage experience I ended up using a small mod that enables marriage for her — it saved me headache and made the relationship feel right. Still, seeing those console flags change felt oddly satisfying.