The targa top from my 76 X1/9 is looking pretty sad. What is type of paint is usually used on these? Can I just have them shoot it with black paint when I have the rest of the car painted? I had also thought about the possibility of having it covered with black canvas like is used for convertible tops. Any thoughts?

There are two versions of the targa top - one is textured and was intended to be left unpainted, the other is smooth and was painted the same as the upper body colour. If you have a 76 then you almost definitely have the textured version.

In order to paint it you would need to get the surface deep cleansed to remove any trace of polish followed by a plastic primer and then whatever colour you desire but you will always have the texture. If you want it smooth you either have to track down a late (smooth, painted) targa or smooth it off yourself.

By way of alternative is the likes of the vinylcote range of plastic paints which go straight on (after cleaning) and change the colour with out the need for a primer but I am not sure they would be hard wearing enough for the targa.

Covering it with canvas would certainly bypass all the above problems but would likely create a whole net set of its own.

If you want it smooth, why don't you remove the trims, shoot it in high build and sand it back to take off the texture. Then apply whatever color you like. Either match it to the car or do something crazy like the Italian red white and green! I must admit though, some colour cars look better with the contrasting black roof.
The canvas idea is cool, just use a bloody good glue to get it down. I'd be worried about it bubbling over time.