In principle.....SEM - EDX can identify the all element in the material (on the surface). In case carbon identification, it means you have to use other coating agents except carbon, for example Gold . However to obtain the accurate measurement, it is better to use XPS or OES instrumental analysis.
Emm... what was the reason that you could not do the EDS? Couldn't observe the samples due to charging (that's one reason to coat the samples, not related to EDS)? EDS signal (x-rays) originate much "deeper" that SE or BSE signals & sometimes due to small size of the powders you're detecting the substrate instead your samples... lowering interaction volume can be done with lowering the acc. voltage of the SEM, but have other drawbacks too..
It depends on (1) which substituting elements do you want to measure (and how precisely), and (2) if this carbon material is stable under the electron beam. In case of "(1)" - some SEMs have special detectors dedicated for light elements (even Li can be measured, which is quite new to the field of the microarea chemical analyses); as with "(2)", you can switch to low-vacuum mode (only some SEMs have this) if the material is easily destructible; nevertheless, SEM is more preferred than EPMA for delicate materials (unless you're about to measure tiny quantities, aka traces, of some elements).
One way to prepare your sample for EDX is drop coating on conducing substrate.
As your sample is powder, you may need to coat it on some conducting substrate, like Si wafer, Cu/Al foil or plate etc. You can make dispersion of powder in ethanol etc and drop coat it on these substrates. Dry sample and use for SEM-EDX.
You can try to obtain (in a metal shop) metal (aluminium is a choice) "rings" (with filled bottom) that would fit to the SEM apparatus you will use. You can then pack the sample into them as you do it with PXRD samples, and then conduct EDS analyses from few areas (or, eventually, linear scans) to obtain the average. This, however, is doable assuming the apparatus (SEM, or rather a classical microprobe) is equipped in a tool available for measuring the COATING (usually if not exclusively carbon) thickness - this thickness must then be subtracted (by a software) from the measured C content. However, most EDS and WDS systems I know can't measure the C content.