Actually, the fossil that appears depends on an odd Factor. According to The Official Pokemon Guide, depending on the end number of your Trainer ID the Fossil that you find can be either one. An even number means you will only find armor fossils, while an odd number will mean you'll only get Skull Fossils, not both. read more
There are: helix, claw, skull, root, armor and dome fossil's and then there is an "old amber" which revives an aerodactyl you can only get armor and skull fossils before you get the national dex but after you get it you can get the other ones as well. read more
Actually, the fossil that appears depends on an odd Factor. According to The Official Pokemon Guide, depending on the end number of your Trainer ID the Fossil that you find can be either one. An even number means you will only find armor fossils, while an odd number will mean you'll only get Skull Fossils, not both. read more
Digging for fossils can take a fair while. In Diamond/Pearl you could only get one of the fossils (i.e. cranidos in one game, shieldon in another). I believe in Platinum you can get both but one is really really rare. read more