There are several ways transform the sound of a guitar into an electric signal. A well known technique uses a coil placed in a magnetic field (the standard singlecoil or humbucker). When an object ( a steel string) disturbs the magnetic field there will be induced a electrical potential (voltage) in the coil. With vibrating nylon it is impossible to disturb an magnetic field because the magnetic properties of nylon are the same as the surrounding air.
The most easy way to amplify a nylon string guitar is with a piezo electric transducer. Piezo electric materials basicly will transform mechanical force to electrical charge. Idealy (for the most natural sound reproduction) we want to transform string velocity to voltage. Maybe this mismatch is that piezo transducers always have a nasty tone like there is a frog singing in your box. You can buy ceramic discs for under the bridge or top, or undersaddle strips transducers.
K&K developped a nice solution of a disc array under the bridge. 4 small piezo electric discs connected parallel. The filosophy behind it is unknown but the sound is great. See Bram Stadhouders with a K&K amplified Elferink nylon string.