Most people have already said what I would say, but the short answer is "no". If I wanted to accept less rent, then I'd lower the rent and put it back on the market and see what kind of people I'd get. Lowering it for you means not only that I can't get someone equally good at the current rate, but not even at the reduced rate. If it comes down to this, then I haven't priced it right to begin with.
I can however definitely see a case where I'd accept an offer for less:
"Hi, we really love your place and would like to rent it long-term. We have perfect credit, perfect rental history, and three times the minimum income needed. We will take superior care of your place and never bug you over the little things, and if there are any big things, we'll let you know about them immediately and work with you closely to resolve them. We will never be late with the rent. Never. Also, we will build a new deck off the back porch at our expense. You're asking $1800 a month; would you be willing to accept $1700 for a 3-year lease?"
That I might consider. Turns out it's never really happened. People who try to negotiate are usually marginal renters who aren't offering anything in exchange for reducing my margins by a hefty amount.