Homemade reactor for water cooling
Unfortunately, many aqueous endothermic reactions involve some chemicals you may wish to avoid.  Ammonium nitrate is the classic example, but in the US it is becoming more and more unavailable because of its potential use as an explosive.  Another frequently mentioned possibility is reacting hydrated barium hydroxide with ammonium chloride, but $\ce{Ba(OH)2}$ is very caustic and poisonous.

So of what I've read, your best choices might be mixing water with a chloride salt like ammonium or potassium.  I do not know how cold this will get your container. I suspect it will not be as good as ammonium nitrate, which would probably be ideal given the former use of this compound in medicinal cold packs.