Is diamond transparent to X-rays?
There are x-rays (Li K-$\alpha$ is 50 eV) and there are x-rays (Uranium K-$\alpha$ 98 keV). 

In reality all electromagnetic radiation tries to pass through everything. Let $\rm I_0$ be the intensity of the beam at the surface and $\rm I_x$ be the fraction that gets through to depth $x$, then: 

$\rm I_x = \rm I_0 e^{-\mu\rho x}$ 

where:


$\mu$ is the mass absorption coefficient, units = $\rm{cm}^2/\rm g$
$\rho$ is the density of the material, units $\rm g/\rm{cm}^3$
$x$ depth of radiation, units = $\rm{cm}$


As a gross generality as the energy of the radiation increases (wavelength shorter) the transparency of matter increases. So a thin slice of carbon, be it graphite or diamond,  will stop the vast major of Li K-alpha x-rays, but very few U K-alpha x-rays. 

Note with some rearrangements and variable substitution this gives the Beer-Lambert Law used in UV-Vis spectroscopy.