Spray think coats, the cardboard will absorb water so you wont get runs like you would painting sheet metal. Once you got the hang of slowly making the cardboard darker you'll have the right technique.
I used to paint weldments in the first shop I worked in. Someone suggested keeping a paint brush handy. If you get a run, it can be quickly brushed out. Also keep the nozzle moving quickly. If you pause the paint will load up and tend to run. Good luck