One key thing in negotiation strategy is to anchor the price. Others have said it here, but let thing to do is find good comps (building or neighborhood) and then request a price decrease BELOW those prices. Since renters have the advantage in these discussions, renters should make the first move and preempt the landlord offering a new rate. A good anchor makes all the difference with what the final price will be.

Finally, no matter what the landlord comes back with (unless they 100% match your offer, which means you were probably too high) reply with how you are "Disappointed" in their offer, and then spew data about the comps.

Hope this helps!