Are diamonds really forever?
how long would it take for this super-material to convert to the stuff
  I scribble with?


No, despite the fact that James Bond said "Diamonds are Forever", that is not exactly the case. Although Bond's statement is a fair approximation of reality it is not a scientifically accurate description of reality.

As we will soon see, even though diamond is slightly less stable than graphite (by ~ 2.5 kJ/mol), it is kinetically protected by a large activation energy.

Here is a comparative representation of the structures of diamond and graphite.



(image source: Satyanarayana T, Rai R. Nanotechnology: The future. J Interdiscip Dentistry 2011;1:93-100)



(image source)

Note that diamond is composed of cyclohexane rings and each carbon is bonded to 2 more carbons external to the cyclohexane ring. On the other hand, graphite is comprised of benzene rings and each carbon is bonded to only 1 carbon external to the benzene ring. That means we need to break 6 sigma bonds in diamond and make about 2 pi bonds (remember it's an extended array of rings, don't double count) in graphite per 6-membered ring in order to convert diamond to graphite.

A typical aliphatic C–C bond strength is ~340 kJ/mol and a typical pi bond strength is ~260 kJ/mol.  So to break 6 sigma bonds and make 2 pi bonds would require ~((6*340)-(2*260)) ~ 1500 kJ/mol. If the transition state were exactly midway between diamond and carbon (with roughly equal bond breaking and bond making), then we might approximate the activation energy as being half that value or ~750 kJ/mol.  Since graphite is a bit more stable than diamond, we can refine our model and realize that the transition state will occur a bit before the mid-point. So our refined model would suggest an activation energy something less than 750 kJ/mol. Had we attempted to incorporate the effect of aromaticity in graphite our estimate would be even lower.  In any case, this is an extremely large activation energy, so, as we anticipated the reaction would be very slow.

An estimate (see p. 171) of the activation energy puts the reverse reaction (graphite to diamond; but since, as noted above, the energy difference between the two is very small the activation energy for the forward reaction is almost the same) at 367 kJ/mol. So at least our rough approximation was in the right ballpark, off by about a factor of 2. However, it appears that the transition state is even further from the midpoint (closer to starting material) than we might have guessed.

This activation energy tells us that at 25 °C, it would take well over a billion years to convert one cubic centimeter of diamond to graphite.

Note 04/17/20: As mentioned in a comment, the original "estimate" link became  defunct and was replaced today with a new estimate link.  However the original article and estimate can can still be seen on the Wayback Machine and it estimates the activation energy to be 538.45 kJ/mol, reasonably close to our estimate.