Diamond at the core of Jupiter
I would think this is questionable, though we don't have a definitive answer yet.

We usually think Jupiter has a roughly solar composition, which according to the solar abundance measurments of Asplund et al. 2009 would mean the total carbon mass of Jupiter is about $10^{-3}$ of Jupiter's total mass. So there's roughly $0.3$ Earth masses of carbon floating around in Jupiter.
Next we need an idea of where this stuff is floating around.  

We know that Carbon is floating around in Jupiter's atmosphere and is enriched relative to solar values by around a factor of $\sim3$, which corrects our estimate of total carbon in Jupiter to roughly one Earth mass, if Jupiter is well-mixed.  

The keyword here is "well-mixed". If carbon atoms stay solved in hydrogen at high pressures in Jupiter's core, then no diamonds can be formed. Only if there is a rain-out similar to helium (see also the phase diagram for hydrogen and helium-mixtures) then droplets or other accumulations of carbon can form, which will be pressed into diamonds.  

The research however at the moment does not focus very much on carbon dissolution at high pressure, so I cannot cite anything reliable on what carbon will do. The reason for this is that the above cited helium-rainout and core erosion which are considered important at the moment.  

I'll try and find some more sources on this as soon as I can go beyond the paywall to the research articles.

Comment on the high pressure-experiments and Juno: To my knowledge carbon-hydrogen mixtures are not being looked at in the labs, but this knowledge might also be flawed.  

Juno will mostly be sensitive to Jupiter's density distribution at pressures up to ~1000 bars. Initial estimates show, that even if Jupiter has a dense, rocky core of 20 Earth masses, this will be barely visible in the data. To then filter out how much is carbon will be nigh-impossible with the current mission.