Trying to creating a plectrum banjo fretboard

[Stan Mulder]

I am not a fretted string player, but I am arranging music for a dixieland
band I play in. I would like to add fret diagrams for the plectrum banjo
player. I think I could do it if it were a guitar part, but plectrum banjo
doesn't seem to be defined in Lilypond. This is where I am lost. I would
like help creating a file I can include to achieve this in my various
scores. I'm not sure where to define the strings/tunings. They should be
tuned: C G B D

I created the following, defining some fingerings, but that's as far as I got:

\storePredefinedDiagram #default-fret-table \chordmode {c}       
#plectrum-tuning  #"o;o;o;3"
\storePredefinedDiagram #default-fret-table \chordmode {c:m}     
#plectrum-tuning  #"o;o;1;1"
\storePredefinedDiagram #default-fret-table \chordmode {c:6}     
#plectrum-tuning  #"o;2;1;2"
\storePredefinedDiagram #default-fret-table \chordmode {c:7}     
#plectrum-tuning  #"o;3;1;2"
\storePredefinedDiagram #default-fret-table \chordmode {c:m7}    
#plectrum-tuning  #"o;3;4;5"
\storePredefinedDiagram #default-fret-table \chordmode {c:m6}    
#plectrum-tuning  #"o;2;1;1"
\storePredefinedDiagram #default-fret-table \chordmode {c:aug}   
#plectrum-tuning  #"o;1;1;2"
\storePredefinedDiagram #default-fret-table \chordmode {c:aug7}  
#plectrum-tuning  #"2;1;3;4" %6
\storePredefinedDiagram #default-fret-table \chordmode {c:7.5-}  
#plectrum-tuning  #"o;3;5;4"
\storePredefinedDiagram #default-fret-table \chordmode {c:maj7}  
#plectrum-tuning  #"o;o;o;2"
\storePredefinedDiagram #default-fret-table \chordmode {c:maj9}  
#plectrum-tuning  #"2;o;o;2"
\storePredefinedDiagram #default-fret-table \chordmode {c:9}     
#plectrum-tuning  #"o;3;3;2"
\storePredefinedDiagram #default-fret-table \chordmode {c:7sus}  
#plectrum-tuning  #"o;3;1;3"
\storePredefinedDiagram #default-fret-table \chordmode {c:7.9-}  
#plectrum-tuning  #"4;3;2;5"
\storePredefinedDiagram #default-fret-table \chordmode {c:dim}   
#plectrum-tuning  #"3;2;1;4"
\storePredefinedDiagram #default-fret-table \chordmode {c:11}    
#plectrum-tuning  #"o;3;3;3"
\storePredefinedDiagram #default-fret-table \chordmode {c:13}    
#plectrum-tuning  #"o;1;3;5" %6

Can anybody help me get a basic skeleton started? Thanks in advance.