You won't be able to save to CXR unfortunately, as CXR is not in the native C4D save menu (at least not as yet). For now you can only save to CXR from the VFB, which would mean the machines would need to run a full C4D with a full Corona license.
If you can get by without saving to CXR, you could do this through Team Render, using the Team Render Server web interface.
https://www.cineversity.com/vidplaytut/cinema_4d_team_render_part_07 might help. You can basically submit jobs, and specify which machines should work on a particular job, so you could assign a different machine to each job and each would work just on that job (so, would render just that one image). This can be done with just one Corona license, and just one C4D license, with the Clients all just being "render slave" machines so they wouldn't need full licenses.
As a note, it will take pretty much just as long to render (say) three images with one assigned to each machine, as it would for each machine to work on the same image at the same time and render the 3 images that way :) The plus to "all machines on one image" is that your processing power will always be doing something, while with "1 different image to each machine", it could be one simpler image or one faster machine will finish and sit idle while the others are still working. EDIT - so, that means you might be just as effective using TR to Picture Viewer from the Master machine, and having all machines contribute to that render, and then you'd also have access to save to CXR.