Ok, so after a lot of thinking I think I've come up with a plausible way to write a triad. The background would be that Fleur had a summer romance with another Veela before Harry, and it's a running joke between Harry and Fleur that he laments not having seen it. So they jokingly made an agreement that Harry would be invited to Fleur's next Veela relationship.
So Harry and Fleur are out in some club, already solidly drunk from their pre-game and a few shots at the bar. So they dance for an hour or so before deciding to take a break in a lounge area, with Fleur sitting on Harry's lap and basically grinding against him. For fun, they start rating people, how they dress, dance, their hairstyle and so on. After a few minutes, they spot Tonks in the crowd and wave her over. There's a bit of small talk which leads to Tonks complaining that she isn't getting any because the good catches are already taken, and, as a single mother and widow at 27, her prospects aren't that great either. So Fleur goes through the "honey, that ain't true" routine, which leads to banter.
After a few minutes, Harry is bored and a bit annoyed, so he tells them to "stop dicking around and kiss already." Due to being drunk, Fleur pulls Tonks down to her, and does exactly that while still wiggling around on Harry's lap. She also makes sure that Harry has a good view of the whole scene and down Tonks dress.
After a few minutes, Tonks makes excuses about needing to go home and leaves in a hurry. Fleur turns around and sees Harry dazed with an expression of Christmas come early. Fleur apparate them home and they make love while describing various fantasies including Tonks and what they'd do to her.
The next day, Tonks shows up to their home and apologies for the previous night, saying that it had not been right and so on. Fleur and Harry draw her into a hug and tell her that there's nothing to apologise for. Fleur then tells her about their fantasies in a husky voice. Add the whole "really? Yes really" thing. She then turns to Harry, who had not said much, and he enthusiastically in confirmation. Tonks then, almost shyly, asks if they really thought about her that way. Tonks still think that they are joking, so they have another make-out session, which ends in her shirt coming off.
Tonks asks them once more if they are sure since she does not want to be a homewrecker. Harry and Fleur share one of these "only with their eyes" conversations before declaring that it's perfectly fine since they both want it and are involved. And that it won't change anything between them. So they have a threesome.
At first, Tonks leaves after they are done, but they have repeats and each time she stays a bit longer. At first, she only stays the night but after a year or so she's basically living with Harry and Fleur, and Teddy has also moved in.
Show a bit of fluff, maybe with Harry still suffering nightmares from the war and Tonks having abandonment issues due to Lupin. There should also be moments which show that they all have relationships with each other (so not only Harry/Fleur/Tonks, but also Harry/Tonks, Fleur/Tonks and a bit of Harry/Fleur). Show them all raising Teddy. Have a scene where Andromeda finds out and her only reaction is along the lines of "well, at least this time you've found worthy partners".
The final scene would be the wedding of Harry and Fleur, with Tonks as maid of honour, who is then screwed senseless by both during the wedding night.
Tonks should NOT end up in a marriage (eg as Lady Black while Fleur is Lady Potter) to symbolise a relationship between three equals rather than Harry + 2 wives and emphasise that their actions/behaviour around each other defines who they are, not a legal document.