Recycle coffee cups for cuttings

I had quiet some success selling my plants but I am in the urgent need to produce more. Short, I am running out of my scrunged pots.
I really don't want to buy a stack of plastic pots and contribute to the plastic mountain we already have. Everything environmentally friendly is prohibitively
expensive.
My idea is asking in a cafe round here, they are using these paper cups to sell their coffee in and I think the size is not bad. But I am selling herb plants and they need
several months at least to reach sellable size. Any idea how long these paper cups last outside in the rain?
Any other ideas? I ask around and will put up a sign that people bring their old pots but I realize that this is not enough.
Newspaper pots don't do it for me.