RC Delay Ciruit for Pi power on
By adding the capacitor C1 you can achieve that. Note that the time it takes before the capacitor empties is roughly R*C, in my example below about 10s. 

The downside of using this aproach is that it will also take as long to turn off the circuit as you need the same RC time. 

A note on your original schematic: the two diodes in series are a very dirty way of dropping the voltage (if it drops the voltage at all), you can better use the resistive divider (R2 and R3) shown in my schematic, with the correct values depending on your battery. 







simulate this circuit &ndash; Schematic created using CircuitLab

Edit: Personally, I would use the UART pin to turn on the circuit and another one to turn the circuit off. You could use GPIO18 to turn off the circuit actually. By having it set as input by default, and only using it as an output when you want to switch off the circuit. Your circuit would then reduce to the one below, with a quick switch off time (R2*C1 = 2s).







simulate this circuit