Sounds like you need a washtub bass
https://en.wikipedia.org/wiki/Washtub_bass
A few years ago there was a three string cardboard bass for sale
http://bogdonboxbass.com/home
They used different gauges of weed eater cord for strings and they sounded decentish. Of course, magnetic pickups are out if you go that route but the piezo buzzer R10 pickup still works.