It seems the most convenient (and also possibly only) choice for a dwg to cnv conversion would be to use Canvas graphics editors that natively works with .cnv drawings and it also can import DWG graphics. Maybe you can use some 3rd party graphics editor or converter for this job, but it's usually always better to use the original software for maximum compatibility.
Convert AutoCAD drawing to Canvas drawing.
We have found one software suitable in our database for this conversion.
Microsoft Windows software - convert dwg to cnv on Windows
Canvas is drawing software used to create technical illustrations and graphics. It is also able publish them via printers, or shared them on the Internet.
Convert from dwg file
to cnv file
The table with program actions contains information about what each program is capable of doing with their files. This may be a good pointer for further searches for certain file conversions and help you find the converter you are looking for if our search result is insufficient for you. However, it is far from perfect and may sometimes show results which are not really usable because of the nature of the software handles the files. So a conversion that appears as possible, just because of matched actions, may in fact not be possible.