We also have blue "trash containers" for recyclables. The city of Los Angeles calls them "trash bins," some people also call them "trash carts," probably because they're on wheels.

Was kommt denn in die "blaue Tonne" rein ? Hier sammeln wir darin Altpapier ... da wäre "waste paper container/bin" eine Möglichkeit ...

From the LA Sanitation page: ... recyclable items, such as: all clean paper (newspaper, envelopes, magazines, cartons, phone books, flyers, etc.); cardboard & corrugated boxes; glass bottles & jars; aluminum cans; tin & metal food cans; aerosol & paint cans (must be empty & dry); all plastics marked 1 through 7 (jugs, bottles, tubs, containers); all clean plastic bags & film plastic (grocery, dry cleaning, packaging, etc.); metal & plastic hangers; aluminum foil & trays; all clean polystyrene products (plates, cups, containers, egg cartons and packing materials).

#1 "Container" or indeed "bin" then.  Thanks a lot!

San Jose, CA uses single-stream recycling, and the bins provided for that (gray with a blue lid) are commonly referred to as "recycling bins" or "recycling carts". See San Jose's recycling guide for details of the items that may be placed in recycling bins. Example usage:

The main thing is to be sure to say what kind of recycling the blue bin is for -- paper and cardboard, for instance, if #2 is right -- because here a lot of recycling is single-stream, so you don't have to separate it yourself at home.

(However, some single-stream is evidently better than others. Looking at #3 I'm envious -- we have to put styrofoam, green glass, hangers, and aerosol cans in the trash aka landfill, take brown or white glass to the recycling center ourselves, and take plastic bags to the supermarket, because none of that is accepted by curbside recycling.)