There are several solutions to your problem. If you're happy to have the smaller output you quoted, just use a power supply splitter circuit like this which will give you +/- 4.5V from a 9V supply:
Another solution would be to just use 2 x 9V batteries to provide +/- (v supplies which would work almost as well as +/-15V but again give you a smaller output swing (probably 6-7V p-p) form your oscillator
Yet another way of doing it would be to get a 9V to +/- 15V Dc-DC converter. On this data sheet
https://recom-power.com/pdf/Econoline/RS6.pdf
is listed type RS6-0515D which takes input 4.5 - 9V and outputs +/- 15V which would restore the p-p output of your oscillator to the original levels.
The lower voltage solutions may need you to tweak some valuse in the circuit to work well at the lower voltages.
