Negotiating in this sort of situation is really simple: You’ve got all the power as long as you’re actually willing to move if they don’t grant you the rent you want. Your willingness to move is a function of (a) the availability of a similar rental for an equal or better price and (b) your willingness to bear the cost and hassle of moving. It’s that simple.
If you’ve found another place that you’d be willing to live that’s a better deal then you should move there if your landlord won’t meet the rent you want.
In general, rents are sticky. They move up and down pretty slowly and down, in particular, really slowly (and rarely). Asking for a 10% reduction in rent probably won’t fly at this stage of the cycle, but might fly in a couple of years. I’ve forgotten what the figures were, but I think that even at the bottom of the 1990s recession here in CA, rents only declined by 12% or thereabouts from peak to trough, and that took 6 years. So, asking for a 10% year-over-year reduction in rent probably won’t work (I obviously don’t know the specifics of the situation, however), particularly if the owner is confident they can get someone in there for roughly what you’re paying now. But it never hurts to ask.
Personally, I’d raise the rent on you by 2%-3%. If you move, you move. I’d get a new tenant and just eat a couple of months rent. No biggie. You gotta remember, if you decide to move, it’s going to be expensive and a pain in the arse – and your landlord knows this. But if you’re willing to bear the cost and hassle, move on.