I have recently read one post over here in chemistry exchange about tastes of ionic salts, some described lead and beryllium ones to be sweet but toxic, some my point is there any salt that is relatively non-toxic (NaCl for example) but tastes sweet (unlike NaCl)
after some searching and a little help from google I have found that Potassium (K) Bromide (Br). In a low concentration of an aqueous solution it will taste sweet. In higher concentrations it will bitter and even salty. wiki The toxicity of Bromide isn't very high and it can be tolerated by a healthy human body under some doses. Yet it's long half-life in the human body make it hard to avoid intoxication (as written in the wiki page).
A question arises, why does the change in concentration affect the taste? I would guess that in higher conc. the KBr distorts the water structure and thus affect the interaction of the ions and cations with the taste buds. I wouldn't use it as a sweetner, and wouldn't suggest tasting it to see the effects of concentration change on the taste.
If we don't restrict ourselves to heteroatomic salts then Sucrose Na is a sweet salt as can be seen here: http://dx.doi.org/10.1016/0031-9384(80)90077-3