I have a 1W push-pull guitar amp circuit where the 9V power supply deliberately sags to ~8V when strumming the guitar. Believe it or not this is important to the sound – it modifies the otherwise snappy pick attack transients.
However, I now want to add another low-load op amp based "preamp" circuit to the same supply but I don't want it's supply to sag. So I'm wondering if there is a way to load the transformer so that the push-pull supply sags as desired but the op amp circuit gets a steady voltage.
Any ideas?
If I add a second rectifier and coupling cap will that suffice?
Or would I just have to go with a separate transformer?
Or perhaps I can use a bigger transformer and then add series resistance to the push-pull supply? But would a resistor act the same? I tried using my bench supply with ~30 ohms in series and got sag but it didn't look the same on the scope. It seems the transformer sag is limited. It seems as the amp pulls harder, the transformer keeps up better whereas with the resistor it just follows ohms law.
Here is a redrawn circuit with a Lm321 IC used as the current limit detector.
The output from the detector could also go to the gate of a SCR, with the Anode going to pin 1 of your regulator and the cathode tied to ground, killing the current regulator output.
I designed and used this circuit in a cnc stepper motor driver circuit. 
Best Answer
The power supply sag, while unintentional, has become part of the "sound" of an amp. Indeed, more modern digital guitar amp simulators actually model that effect.
But, for your question, this issue affects the main output power amp than op-amps.
Op-amps have a specification, called PSRR, or Power Supply Rejection Ratio. This gives you some indication on how much noise on the power rails will be coupled to the output of the opamp. Normal opamps have a medium to high PSRR, while power amplifiers have a much smaller PSRR.
If I were you, I would first choose an op-amp with a high PSRR and just try it with your droopy rails. Odds are high that you won't have an issue with just that. But if you still have issues, then you will have to filter and/or regulate the droopy rail into something that works better.
If this were my project I would put an LDO linear regulator to take the droopy 9v rail and bring it down to a nice and quiet 7.5v.
A transformer and rectifier only helps if your 9 volt rail is AC and not DC. You didn't specify which it is, but I am assuming DC because if it is AC then you are looking at the wrong thing.
Other than that, it is impossible to tell you what to do without seeing schematics for the amp that you have, plus schematics for what you want to add.