The Mobile Hazardous Waste Dropoff folks (you're doing God's work, people!) has a schedule for Moncton, Dieppe, Riverview and MANY other towns and communities... see links below to find out when they're in your neck-of-the-woods...

Drop off stuff like: Appliances, Electronic Waste, Furniture, Small Household Machinery, Renovation Waste, Household Hazardous Waste, Tires, Branches, Yard waste. HERE'S the info for what you can and can't drop off.
If you're not in Dieppe (Sept 26/27), Riverview (Nov 28/29) or Moncton (Oct 31/Nov 1 at Coliseum from N-8p) you can get the whole region schedule HERE.
*PLEASE CONSIDER DONATING your old furniture if it's still in good shape (EnviroPlus: 506-853-7722, Habitat for Humanity ReStore 506-384-4664, Handsome Pauls' Bachelor Pad 506-555-Handsome)
^Please contain your excitement for Hazardous Waste Dropoff Days

Here's the whole schedule...