Leaflet Markers are stored as files unlike other objects (like Polylines, etc.)
If you want your own markers, you can find The official Leaflet Tutorial that explains how to do it.
EDIT :
After reading this conversation with the main developer I searched for the marker SVG and here it is.
With this you should be able to color the marker the way you want and randomly set their color.
EDIT AGAIN :
You can also use MakiMarkers to set the color of a marker and use this extension to make some random stuffs. (It's simple and well explained)