I have a GE clothes dreyer making a nasty squeak and gets worse the heavier the load. The belt and pulleys are good. I recently sprayed the belt with belt dressing and also a single squirt to the center of the tension roller at the shaft. It stopped for about a week and is now back with a vengeance. Question: what kind of lubricant or grease can I use at the center of the pulley at the shaft (preferably a spray) that will last??

You will find no luck with sprays. They are lighter and thus dry up quicker, not to mention the aerosols that help it. I would suggest a heavy lithium or graphite axle grease.

Use synthetic turbine oil. I use Amsoil RCH05 Synthetic RC Series R&O (Rust & Oxidation)/AW (Antiwear) Gear, Bearing, and Hydraulic Oil (ISO 32/SAE10). This is an industrial lubricant that is not readily available. I use it to lubricate all motor bearings, up to 5 h.p. It's a superior R&O oil for lubricating A/C condenser fan motors and dryer applications, among many others.

You may want to try the following turbine oil product, which is readily available:

Zoom Spout Oiler, Blue Lake Products, 4 oz. Unocal 76 Turbine Oil (ISO 32), 7-1/2" to 13-1/2" spout, available at ACE Hardware, $1.75. It is not a synthetic product, however.