Hi Weeder -
There isn't really a "good" fabric tape from a conservation point of view.
If your painting is in reasonably good condition Hanna's ideal of very light tensioning via stitches or pins is probably the best.
There are a number of methods for this. I like the fabric covered padded backboard with the edges pinned or stitched to the fabric/padding.
I try not to wrap the edges of the art textile around to the back, as over time the edge of the backboard puts a lot of stress on the textile and cracks/breaks develop. If one really needs to wrap the edges of the textile to the reverse of the backboard, the underlying padding can be wrapped around to the back as well, so that the edges of the backboard are softened.
The nice thing about this method is that it is easy to adjust centering, tension etc.
For very fragile pieces Jim's crepeline/Stabiltex overlay technique is good, but the image is obscured a bit. Pressure mounting might also be an option in this case.
Too much information eh?
Have fun!
Rebecca