Silvosol is a product available in Europe that effectively removes silver nitrate stains (see this video by Borut Peterlin). However, it's difficult to get in North America without exorbitant shipping fees. Luckily, looking at its SDS gives us the three ingredients it contains: phosphoric acid, thiourea, and tartaric acid. These three chemicals can all be easily and cheaply bought from eBay.
The ratio of the chemicals is not given exactly in the datasheet, but a solution of about 1 part tartaric acid, 2 parts thiourea, 2 parts phosphoric acid, and 25 parts water will work.
To make 250mL of solution, you will need the following:
7.5g tartaric acid
15g phosphoric acid
Water to make 250mL