This is tough one. First, you need to find where the squeak is comming from, and that is not easy. The squeak could be a bearing on an idler or tensioner pulley, however, you say that when belt dressing is applied, the squeak goes away for a short time. This indicates that the belt is skidding on a pulley or sheave.

The belt can skid on an idler or tensioner pulley when these are not running true with the belt. The most suspect item is the tensioner. An old tensioner can go out of alignment from wear and use.

The second cause is the belt slipping on a sheave. The little V's on a serpentine belt is supposed to contact the sides of the v-grooves and the belt should not 'bottom out'. If the v-part drops too deeply into the grooves, the contact surface transfers to the bottom of the v-groove and to the top surface of the sheave. The belt looses its grip on the sides of the Vs and slips. Examine the bottom of the v-grooves on the belt. If these bottom lands are shiny, this indicate they have been contacting the outer diamenter of the sheave.

The remarks above refer to a serpentine belt with multiple, small Vs on it. Should your engine use the older v-belts, the part about a serpentine belt slipping from wear or misfit does not apply. For older V-belt design, a new belt on a servicable sheave will ride with its top surface above the outer diameter of the sheave. As the belt wears, the top of the belt becomes flush with the sheave and when worn out, it will be below the outer diameter of the sheave. Often, other signs of wear will show before the belt sinks to below the sheave's outer diameter.

If it's a V-belt, it's probably skidding over the alternator sheave. Though alternators spin real easy by hand when the belt's not attached, they pull pretty hard when in operation. If you're desperate to try something besides trying to pull the belt tighter, try replacing the sheave on the alternator. I doubt a belt from the dealer is any better, and maybe not even any different than the one from NAPA, assuming they gave you the right one in the first place. Length of the belt is one thing, width is equally important.

I think there is a build up of varnish, oils, dirt,rust, on the pulley contact surfaces, which may have been accumulating for nigh 20 years.
I clean the pulleys using scotch brite and a little paint thinner - on the VW, no problem with the Honda - yet..
And the new belts have to be adjusted at least once, and tight, tighter than I like..
And Gary has made a good point - you may not be using the correct belt...