There is nothing in the standard Image class to handle PNG files; and I know of nothing that can handle the conversion - since JPG are full colour and PGM are greyscale, that doesn't surprise me. And given that is is an uncompressed, very basic file format, I am not surprised by the general lack of support.
So probably, you will have to write your own.
These two links should help: PGM File specification
Reading-Writing PGM(Portable Graphics Media) Image Files With C#(C Sharp)
But do not expect the C# code to be a complete solution: it very definitely isn't! You are very much on your own with this one...