Op-Amp based power supply, what powers the Op-Amps

Assuming at least one of the power supplies is isolated (which will be true if they are good power supplies, but maybe not if they are cheap), you can make a stack of two supplies, so you have outputs at 0 V, 9 V and 18 V. Then, connect your op-amp circuit like this:

• Power supply 18 V -> 9 V op-amp pin
• Power supply 9 V -> 0 V op-amp pin
• Power supply 0 V -> -9 V op-amp pin

Another way to think about this is to understand that ground (0 V) is a relative choice; you can change your choice, as long as you're consistent within one circuit.

One other note-- I should explain what I mean by "isolated." A cheap power supply will have its ground pin connected to the neutral wire of its power cord. Most of the time, that's fine. But if you want to stack supplies, you need an isolated supply, i.e. one where no output pin is connected internally to the power cord.

If you do try to stack non-isolated supplies, you'll be connecting the positive output to the neutral wire, which is the same as shorting out the supply, so its internal fuse will blow. (If it's a really cheap supply, this will destroy it.)

One other solution

If you can't lay your hands on an isolated supply, you could use a switched capacitor voltage converter. This is a chip that charges up a capacitor, and then quickly shifts the pins so what was previously the positive lead is connected to ground, and the old ground becomes a negative output. It does this charge/switch routine at 10-100 kHz, so to humans, it looks like a negative supply.

Are you sure your routers take 1.5 amps at 120v? It seems far more likely to me that they use 1.5 amps at 12v or less, which means your AC power strips only have to supply say 0.2amps per router.