Set ground reference of a 5v DC power supply to the middle of a 24v DC power supply
Neither work well. 

The first is the right basic idea, but a normal opamp doesn't have enough power, so if your analog circuit dumps more than a few mA onto the GND connection, that exceeds the opamp's output current, and the opamp loses control so that GND is no longer halfway between the supplies.

The second one works if the analog circuit pulls current out of GND (think of a resistor between GND and -12V) but not if it sources current into GND (resistor between GND and +12V). In the latter case, GND will be pulled up towards the +12V rail.

If you use the first idea, but replace the opamp with an amplifier capable of supplying 1 Amp (or whatever your PSU is rated for, you didn't say) you have a good basis for a solution. (Add a decoupling capacitor across each of R1 and R2 to reduce noise). But such an amplifier may be quite expensive and require a heatsink.

Frankly the simplest solution is separate +12V and -12V supplies.