The only approach that one uses with human beings is based on beta cells/islet response to insulin secretory stimuli (primarily glucose). This method has its limitations because of obvious reasons where altered secretion or function of insulin for any reason will effect the secreted insulin levels and given that there is considerable reserves of insulin, in a typical test duration, it is difficult to reliably link the insulin levels (are under the curve etc.) to a specific number of beta cells.
Even if invasive procedures procedures could be contemplated, needle biopsy is not very likely to give an overall picture due to difference in composition of islet cells between head a tail of pancreas.
As you alluded to, in experimental animals PET has been used for estimates islet mass by loading the animals with labeled compound (dihydrotetrabenazine and fluoropropyl analogue - DTBZ) that target vesicular monoamine transporter in beta cells. I do recall a clinical trial by Columbia U but I am not sure about the outcome. Perhaps you could search through NIH website.
You may want to give the following review a quick read: