Adam,

You're right again! Unfortunately the paper is no longer on-line but the reference is:

"Phase diagram of carbon at high pressures and temperatures" by Matthew P. Grumbach and Ricard M. Martin, 8 Nov 1996. (journal not known)

On Figure 16 there is a PT phase diagram of carbon with a Jupiter adiabat. The Jupiter adiabat never goes through the diamond phase. Instead it goes directly from the graphite phase to the liquid carbon phase. The Jupiter adiabat actually achieves pressures greater than those required for diamond but the temperature is too high for diamond to form (it's "liquid diamond" as you said).

Gary

p.s. The Earth's adiabat goes through the middle of the diamond phase. There must be heaps of diamonds in the Earth's mantle. Also, diamonds are not that uncommon in meteors.