I am looking for a non-toxic, water-soluble chemical, or solution,
that has a PH of 9.0 or higher when it is liquid but rapidly drops
below 7.0 when exposed to air.

You could try something like this.

4 Ti(OH)[2+] + O2 + 2 H2O = 4 TiO2 + 8 H[+]

You would only need micromolar level basic titanium(III) solution for
this to work but it would be difficult to keep such solutions from
reacting with air unless they were sealed in an ampule.

You may try to use amonium water solution (NH3.H2O)to adjust the pH.
NH3.H2O is a base liquid(pH>7). NH3 gas eventually will escape from
H2O in 1 atmsphere and leave the water neutral(pH=7).

People use this trick to make inks. When ink meet air NH3 escapes and
the system is neutralized, the polymers inside precipitates and
becomes a dried ink coating later.