Whew. Now that would be difficult.
Well, if you wanted you could have them make a ship or ship cluster approximately as large as the moon, because that is large enough to block the sun at the distance it's at. The other two options are making it larger than the moon and farther away, or making it smaller than the moon and closer, obviously. I have a feeling the second one would be considerably easier, however I'm not sure how outer you want the 'outer space' the villains control to be. Closer than the moon isn't that far out, on a galactic scale, but it's plenty far enough to be 'outer space' if you're talking more along the lines of taking over space stations, satellites, etcetera. Hm.
And it wouldn't block the sun in very many places, either, like a solar eclipse.
If you wanted to go, like, full out on the impossibility scale you could even try something like a solar dyson sphere. That would be cool. Depending on what model you fixed on it could definitely block off the sun, or at the very least shade it and make it look mighty odd. And if you did the satellite-array sort of thing, then it might not be entirely out of the realm of feasibility, even. And anyway, these are supervillains.
But if it had to happen suddenly, something on the scale of a dyson sphere would be a bit difficult. I think the most dramatic way possible would be for them to create the vast amount of ships needed somewhere a short distance away from the sun (you know, Venus or something) and then fly them out all at once. The vast amount of ships needed would make it basically impossible to have very many of them on earth, or build them on earth, or anything like that; I'm not sure it would be possible even if you stacked them up over every available earth surface, and that would be slightly noticeable, if you know what I mean. That is, unless the satellite-array they put up is very spread out, taking up less ships, which wouldn't even be noticeable.
Unfortunately, I doubt you could even fit them all on Venus even without anyone there to be noticing that it's all covered with space ships. I don't know, I guess it depends, again, on how spread out the satellite shield would be.
I know there is some way to calculate approximately how many square miles of ships you would need to make the shield, but I don't want to think that hard just now....
If you did a solid-sphere sort of idea, than you really couldn't have it go up in one day.
That would be... unbelievable, even for a supervillain series. At least to me. 
But if you wanted to make it a little easier, it could be not exactly a sphere... maybe a belt of some kind? That would be noticeable, still, if it was broad enough. And, if it was broad enough, it would at least lessen the sunlight, maybe?
But the whole dyson sphere thing has problems of its own, especially the closed-sphere. Like, gravitational collapse and stuff.... So... maybe it could be made more possible by a superpower? Something... magneticky, or something. I don't know.
Compared to a dyson sphere, my first idea was more feasible.
But it doesn't have has much of an effect. Also, I can't see as much of a reason behind it.... A dyson sphere is like 'I'm stealing the sun!', but the first idea is just like 'I'm putting a great big thing in the sky that covers the sun in various places on earth at various times!' Oh, what if, instead of covering the sun, you covered the earth? That would still block out the sun, obviously. Heh. But it would be more feasible. And there could be some interesting things the supervillains could do with a screen-sort surface that big..... * grins *