I strongly suspect that Tarkin knew full well that to take out Palpatine he would have had to blast Coruscant to little bits. he was also intelligent enough to realize how many problems that would have created. I think it is far more likely that Tarkin's long-term goal was considerably less drastic - he didn't want to overthrow Palpatine, he wanted to become his heir. Tarkin had already acted in the role of successor to Imperial control during the Ghost Prison incident. He's roughly twenty years Palpatine's junior and the Force aside, the Emperor was never exactly a glowing vision of good health. This is a generally neglected point of EU speculation, and it seems likely that Palpatine was deliberately extremely vague on this point, but various high-placed IMperial personnel had to have thought about it a lot. We should remember that it was Tarkin, more than perhaps any other being in the entire galaxy, who actually believed in the Empire. Even Palpatine himself simply wanted the Empire to serve his own ends, but Tarkin truly thought the Empite was a better means of government. Overthrowing Palpatine would likely have destroyed the Empire, and that was an outcome Tarkin did not desire. I view Tarkin's command decision to destroy Alderaan as a declaration of his power and authority - he did something that really, only the Emperor ought to have been able to order. If he'd destroyed the Rebellion shortly thereafter though, he'd have gotten away with it, and Tarkin knew that, and if Palpatine has to allow the man-who-detonates-core-worlds to continue running his mighty battlestation then Tarkin has moved into a de facto position of superiority over everyone else in the Empire.