I am not sure why you are opposed to the RTC or whether you were excluding all external circuitry for the solution. So, I am just throwing this out there...
A CMOS-4060 ripple counter can be programmed for just about any time period and using two of them would give you two separate time constants.
source Substitute the relay for a signal wire to the CPU.
The Cmos 4060 is a 14-bit binary counter. However - only ten of those bits are connected to output pins. The remaining bits - Q1, Q2, Q3 and Q11 - do exist. You just can't reach them.
The 4060 also has two inverters - connected in series across pins 11, 10 & 9. Together with R3, R4, R5 and C3 - they form a simple oscillator.
While the oscillator is running - the 14-bit counter counts the number of oscillations - and the state of the count is reflected in the output pins.
By adjusting R4 you can alter the frequency of the oscillator. So you can control the speed at which the count progresses. In other words - you can decide how long it will take for any given output pin to go high.
When that pin goes high - it switches the transistor - and the transistor in turn operates the relay.
In single-shot mode - the output pin does a second job. It uses D1 to disable the oscillator - so the count stops with the output pin high. .
If you want to use the timer in repeating mode - simply leave out D1. The count will carry on indefinitely. And the output pin will continue to switch the transistor on and off - at the same regular time intervals.
For example, if you want a period of 9 Hours - the Range table shows that you can use the output at Pin 2. You need Pin 2 to go high after 9 x 60 x 60 = 32 400 seconds. The Setup table tells you to divide this by 512 - giving about 63 seconds. Adjust R4 so that the Yellow LED lights 63 seconds after power is applied. This will give an output at Pin 2 after about 9 Hours.
If you increase the value of R3 - and reduce R4 by the corresponding amount - you can set the time delay more precisely. Select a value for R3 that takes you close to the time you're after. And use the reduced value pot - to make the fine adjustment. Note that even finer adjustments are possible with a multi-turn pot.
As mentioned with VE7JRO's solution, this solution (while being pretty accurate) will eventually drift with time and must be powered up at an exact time that is synchronized with the desired trip times.