Bind in the icons from this site!
https://github.com/pointhi/leaflet-color-markers
Detailed how-to information included on the website.
Edit: Use the code below to add a marker icon and just replace the link to the one with the color of your choice. (i.e. marker-icon-2x-green.png
to some other image)
var greenIcon = new L.Icon({
iconUrl: 'https://raw.githubusercontent.com/pointhi/leaflet-color-markers/master/img/marker-icon-2x-green.png',
shadowUrl: 'https://cdnjs.cloudflare.com/ajax/libs/leaflet/0.7.7/images/marker-shadow.png',
iconSize: [25, 41],
iconAnchor: [12, 41],
popupAnchor: [1, -34],
shadowSize: [41, 41]
});
L.marker([51.5, -0.09], {icon: greenIcon}).addTo(map);