Luvdisc can learn Entrainment. Use it on a Rain Team to give something Swift Swim that normally doesn't have it. I have no clue how competitive battles work for doubles/triples though, so I'm not sure if this would be good...
Same could apply for Leavanny/Lilligant and Chlorophyll for Sun Teams.
"Combine Cloak and Dagger with Boots of Swiftness so CC doesn't stop you from moving faster toward defeat." - Frost_shock_FTW
This is kinda outclassed by other speed boosting moves in doubles, Tailwind in particular.
Tailwind boosts your entire team, not just one Pokémon, Tailwind isn't dependent on you keeping your chosen weather, and there are Pokémon with Tailwind who are much, much better than Luvdisc. I mean that goes without saying, but really, there are some superb doubles Pokémon who get Tailwind like Latios, Tornadus, and Volcarona.
I think it might make for a cute gimmick/troll team (it's certainly the most creative idea for using Luvdisc I've ever heard, and probably the best use you'd get from Luvdisc in doubles) but I don't think it has any actual competitive use.
@above, Entrainment doesn't work on pokes with Truant