I need two chemicals, preferably both liquids, that will combine to
produce an endothermic reaction in which the solution will drop to
freezing or below and maintain that temperature for between 30-60
minutes.  The chemicals, and the end solution, need to be non-toxic
and able to be stored safely in a plastic container.

You may find the chemicals that combine in chemical ice/cooling packs
to be helpful, but I have found that, in most cases, one of the
chemicals is in a solid state.  While I suppose I could work with
this, I really need two liquids.

Here is a website that sells a chemical ice pack and lists the
ingredients... this may be a helpful start:
http://www.dual-ice.com/Safety/safety.html

I suspect that you are going to need to use a system that ultimately
involves a phase change (i.e., dissolution or precipitation of a
solid).  The reason being that for any two liqids that do not result
in a precipitation reaction upon mixing, the enthalpy of the mixing
reaction is going to be rather modest.

Most "chemical ice packs" that I am familiar with involve the
endothermic dissolution reactions of a salt, such as sodium
thiosulfate or ammonium nitrate in an aqueous solvent.