Actually PSP can do 32 bit TGA's (at least 7 can anyway)
You just need to save an alpha channel manually before saving.
Create your image on a layer or layers
Merge to one layer
Ctrl-A to select all
Click the mouse on a part of the image
The whole image gets hilighted without background
Selections->Save To Alpha Channel
Save as a new channel (doesn't matter what you call it)
Save as a tga. If it worked you'll get a warning that it's only going to save one alpha channel.
Note this will automatically set the transparent area to white. You may want to fill a layer with black and put it behind the actual image layer before saving if the translucent image shows too much white in the semi trans bits.