Correct diode for this application
The circuit can't work exactly as shown, there needs to be a load from the output to -5V that is much higher than 2K, say 100K, There should also be bypass capacitors across the two supplies, near the chip. Something like 100nF each, or you could get oscillation. 

It should work with either of those diode types you tried, or with Ge or Schottky diodes, the only difference will be slightly different output voltages. With the two you tried, the output voltages should be a bit (~0.4V) lower than than with the Ge diodes at 0V and +5 (perhaps -0.8 and +4.1V with a light load to -5V, rather than -0.4 and +4.5V). To get similar behavior to the Ge diodes, you could use a Schottky diode such as the BAT54C.