I have an old bike with a Suntour Cyclone derailer on it which seems to be nothing but trouble. I have tried adjusting everything on it with little success. It seems to make noise no matter how much I trim it. When I get on the pedals hard I can here it making a sound like the chain is trying to jump gears. Lubrication does not affect the noise level. Im not sure what to do except just replace it.

Is this a friction or indexing system? Are you sure it's the derailleur, not a badly worn chain and/or cassette/freewheel?

It is a friction shifter. After going over Sheldon's chain maintenance section I'm still not sure. The bushings seem rather loose on the rivets to me though. I would think the teeth on the sprockets would be worn if the chain is bad but they look good, the ones on the cassette are still flat on top. Maybe someone put an old chain on this bike for some reason.

How is the alignment on the hanger? Looking from the back does the RD pulleys align with the cogs in a plumb line or does the lower pulley look closer to the wheel than the top pulley?

The lower pully is closer at the bottom. I fiddled with it and it looks like there is some play in the roll pins on the joints that allows the hanger to bend in at a slight angle. So I'm thinking I need a new chain and a new derailer.

A new RD may help but the rear hanger may need to be bent back into shape to properly align everything.

Most (decent) bike-shops have a special tool, such as the Park Tool DAG-2, to properly straighten the rear hanger. Shouldn't cost more than $15 to diagnose and repair.