When I am idling it runs fine, and l give it gas and sounds okay but as soon as it idles down, it backfires a small bit. What is causing this? We have already changed the plugs and wires and put a new fuel filter on it.

you need to check and adjust the timing.

l am guessing you mean 'after-fire'' which is through the exhaust. Backfire is back through the intake.
Anyway this condition may be caused by a fuel rich condition. If the engine has fuel injection, perhaps one or more injectors is leaking. Did the old s/plugs appear black around the electrode? If so, consider having the injectors tested and professionally cleaned.

l had this problem too in a 1994 3-cylinder engine.very significant after-fire & lurching when attempting to accelerate from a stop.

l am sorry to say that it is usually caused by burned & warped exhaust valves, particularly in the number 3 cylinder (the one closest to the distributor). This can be corroborated with a vacuum gauge; if the gauge is shaky at idle, then u have a bad valve.

Swapping with a re-manufactured valve head (plus a new gasket) will get u going again.

If u hear an occasional (very faint) ''backfire'' in the exhaust at idle, this is normal. Mine did it since it was new. l was told it is due to the inherent imbalances of a 3-cylinder engine.