One way is to "fill in" the C with timber then use regular joist hangers. The infill is bolted to the web. I think you can get tall hangers that can be wrapped over the top of the beam and fixed to a similar infill on the back - or at least to the timber/purlin between the back to back C channels. Just remember that joist hangers rely on "end restraint" (eg at the other end of the joist) to stop the heel of the joist pulling out of the hanger.

Is it just one joist?

If it's a bolted two C channel, it's unlikely to have a torsional rigidity problem and also unlikely to need effective lateral restraint. Joists rarely have critical shear at the bearing. Ask your engineer, but you may be able to just shape (jigsaw) and wedge the joist.

If the joist hanger is made fast to the top of the C beam, once the joist in put in it all will be well, the trouble is that with loading and vibration the bottom of the hanger will move inwards into the C and the joist will want to slide out. So the thing to do is to stop the bottom of the hanger bending inwards. A piece of wood (4" X 2") of the length of the depth of the C and fastened at the bottom of the hanger going into the C will stop this happening. So cut your piece of 4" X 2" nail in to the back of the hanger, by a nail through the back of the hanger and hang hanger. If you put a piece of wood at the top of the hanger's back, this actually takes no load because the top of a joist shortens when it is loaded.
3" or 2" wall plate - depends on how far apart your fixings are for the wall plate. 2" should do if the fixings are at the joist spacing.
Frank

Agreed; Timber.
marsaday, If you want to be very fussy about shaping the ends of the joists precisely to allow for the steel shape, simply make by hand a simple MDF template, and just transfer the shape to each joist end, perfect fit every time. If you're plasterboarding onto the underside, cut the joists to underhang the RSJ very slightly, so that the subsequent plasterboard is just off the steel.