Can you set up a monostable 555 timer so it reverses the output?
I think if you use a second 555, also connected as a monostable, but replace the timing capacitor with a short (and you don't need the timing resistor)-- triggered by the first one, that should work. 

You could also use a D flip-flop such as a 4013 with the D tied high, but you'd need an inverter on the clock and a power-on reset circuit. 

Or, something like this: 







simulate this circuit &ndash; Schematic created using CircuitLab

C1/R3/D1 provides a semi-reliable power-on reset (100% reliable if the power turns on cleanly every time after a relatively long 'off' time where +V falls to near 0V). 

C2 and R4 provide an edge trigger from the 555 output falling edge. 

R1 and R2 protect the CMOS inputs