In her book, "Garden Ornaments," author and garden designer Martha Baker likens the mold and age spots on antique stone garden ornaments to the rich patina of antique wood furniture, because both display character and enhance an object's value. Fortunately, it's easy to give a new cast-stone or terra-cotta planter an aged look with a wash made of one part water and two parts latex exterior paint or latex stucco paint.
The paint color will depend on the effect you're trying to achieve. Moss green looks, unsurprisingly, like moss; blue-green resembles oxidized copper. Brush the paint mixture onto the planter, then rub it off with a damp sponge so that the residue is left in the cracks and depressions. You can also try layering several colors: Apply a coat of white, then moss green, then black, wiping off the object with a damp sponge between coats.
Martha Baker's "Garden Ornaments: A Stylish Guide to Decorating Your Garden" is available at Amazon.