Can oxides of uranium be used to color aluminium oxide based gemstones, or diamonds? Rubies and sapphires are chemically equivalent to the mineral corundum, with the exception of transition metal impurities that impart different colors to the aluminium oxide. Uranium is not a transition metal, but it can be used as a coloration admixture with silicon dioxide, and exists in various oxide forms.
Can uranium be used as a coloration impurity for 1) aluminium oxide based gemstones and/or 2) diamonds? If uranium cannot chemically bond with the substrate, then the ability to produce a consistent heterogeneous mixture, e.g. by suspending uranium oxide dust in molten aluminium oxide during the process of flame fusion would be a satisfactory answer in the affirmative.
 A: The most uranium-rich oxide phase is uranium dioxde, UO$_{2}$ which forms in the calcite structure. So it can be at least suggested that uranium is not going to particularly like to sit on an Al site in Al$_{2}$O$_{3}$, although this does not, of course, rule out the possibility of a uranium-based color center being formed in association with a defect (Al or O vacancy, for example).
A 1953 paper in the Journal of The American Ceramic Society investigates the UO$_{2}$ - Al$_{2}$O$_{3}$ phase equilibrium. While concentrating on the liquidus, it does state in the Discussion

there was no indication of any solid solution or new phases being formed.

Furthermore, there are a number (well, not a lot) of papers in the literature using U-Pb dating to determine when ruby/sapphire deposits were formed in different places, such as this one in Mineralium Deposita. However, they don't try to measure U and Pb in the corundum itself, but rather look for inclusions such as rutile and measure the U/Pb ratio there. This suggests that U just is not particularly soluble in Al$_{2}$O$_{3}$.
The classic paper on coloring glass with uranium is in Optica from 1945 which details which U-O structures lead to particular colors. None of those structures appear to be particularly compatible with the sapphire crystal structure.
Without further data, it is unlikely that trying to dope sapphire with uranium is going to be successful. Further, there do not seem to be any known color centers in sapphire based on uranium.
For diamond the literature is even scarcer. While green-tinted diamonds are associated with uranium ores, that is only because the uranium is the natural source of radiation that induces the green color centers in the diamond. However, uranium is not actually a component of that color center.
