I've tried this and my obstacle has always been cleaning and assembling the models. If I ever manage to get my speed painting down to, say, 20 minutes per model, it still takes 20 minutes to assemble them and clean the mould lines. If you left the mould lines it'd be more practical, but I'm OCD about mould lines.
But yeah, that aside, a terminator army, or maybe a grey knight army.
Another option is a Tyranid army, which may sound strange, but you can just spray them one colour, use a big brush to roughly paint the carapace red or blue or whatever, then dip them.
If you ebayed an already constructed but unpainted army you could save yourself a lot of time as well. Necrons are the sort of army you could PAINT in a day, but the way the models are designed it'd take another day or so just to assemble them (I don't know who had the brilliant idea of putting the injection points for the heads on the cheeks!!).
Another option might even by a Cadian army. That may sound insane because it has heaps of models in it, but you can actually paint them quite quickly as they have a simple colour theme. Leave off the bags and knives and they paint even faster. Then just do a couple of Leman Russes with sprays and drybrush/wash with a giant brush. Again though, the painting time you might be able to get down to a day, but the assembly is gonna take a while (I think my Leman Russ took me the better part of a day JUST to assemble).
Anything which can be reduced to 2 or 3 colours, the first of which is sprayed, has potential to be painted quickly though.