While your credit score is important, landlords generally do not make a determination based on that alone. Employment history, length of time at your current job, income, and references all play an equally important (if not more important) part. The fact that you would be willing to put down a larger deposit, and/or pre-pay a few months will definitely help also.
My suggestion would be to be as honest as possible when applying. Write a short letter to accompany the application, detailing your situation and the circumstances that are "driving" your less than perfect credit score.
As a rental property owner myself, I understand that it's unrealistic to expect everyone to have an 800 credit score. If someone applied who had an unpaid medical bill 5 years ago on their credit report, I'm going to obviously weigh that differently than someone who has recently racked up 5 credit cards and is running from creditors.
Everyone makes mistakes. My credit report was haunted for years by a check I bounced in college from a pizza I ordered at 2AM. Explain your situation - and highlight the fact that you have sufficient income and stellar references from previous landlords. That would, in my opinion, carry much more weight than a mistake you made 6 years ago. The landlord really just wants to know that at the end of the day that currently, you will be able, and willing, to pay your rent when due every month.
Hope that helps!