You shouldn't require this number for a well-designed circuit. For light loads on a CMOS output timer you might be able to find a number, but generally it's variable with power supply voltage, state (it's asymmetrical) load, temperature, unit-to-unit etc. and there will be a big nonlinear component in bipolar output timers even with a light load.
If you want a controlled output impedance add some resistance such as a few K ohms to the unknown (but very low) resistance of the timer output.
A TLC555 has "typical" output resistance of about 80 ohms (high, at 10mA) and 12 ohms (low, at 10mA) with a 15V supply. With a 5V supply it's 200 ohms (high, at 1mA) and 25 ohms (low, at 3.2mA). If you connect a capacitor directly to such an output your predictions will be way off if based on those resistance values since the MOSFETs do not behave like resistors when their drain-source voltage gets close to the threshold voltage (they behave more like constant current sources).
I generally use 50-100 ohms for the open-loop output impedance of an op-amp. Sometimes a typical value is given on the datasheet.