Actually it turns out I’m wrong because simple math is hard.
Ideal gas law says that for a body of ideal gas at constant volume, the pressure and temperature are proportional. This means that you can calculate pressure and temperature changes like this:
P1 / P2 = T1 / T2, or P2 = P1 * T2 / T1
The trick is that all of those values have to be expressed in absolute. So for a tire starting out at 35 psi-gauge, P1 = 35 + 14.7 = 49.7 psi-absolute. And if it starts out at 75°F, then T1 = 75 + 459 = 534.
Now we drop the temperature ten degrees, to T2 = 524. So our final pressure is:
P2 = 49.7 * 524/534
P2 = 48.769 psi-absolute, or 34.07 psi-gauge. (I forgot to switch the tire pressure to absolute, which is why my earlier answer was wrong).
So yep, about 1 psi per 10°F is the correct answer, assuming we’re dealing with typical car tires that are inflated to 30-35 psi. The 2-psi figure is a better match for truck tires, which are typically inflated to ~100 psi.