If you don't need isolation and can live with ~+/- 10v (should be perfectly fine for rs232) , you could also use a couple of voltage doubler/inverting ICs
ex. see
https://www.digikey.com/product-detail/en/microchip-technology/TC7660SCPA/TC7660SCPA-ND/418702use one for 5v->~2x5v and 2nd one for 10v -> -10v
All you need is bunch of ceramic caps and diodes around these DIP ICs.
edit: the circuit in your picture seems like it takes 5v and makes+/- 6v .. but isn't rs232 +/-12v? I think the minimum threshold was +/- 8v that's why i said +/- 10v should be fine.
for +/-5v you'd only need one chip in inverter mode and theres cheaper ICs for that with max 5.5v input voltage, like max1720 for example
A more flexible (adjustable output voltage, so could have +/- 6v or +/-12v) would be to use two *33063 *34063 switching regulator... super cheap, available in DIP, can use lower switching frequencies to make circuit on stripboard, online calculators and freeware software on sourceforge to tell you component vales if you don't want to use formulas in datasheet.
Requires inductor, diode and a bunch of ceramic caps and resistors but for 10-50mA you would possibly need for rs232 these should be super cheap. Probably less than 1-1.5$ for two , one in step-up mode and one inverting mode (neg. voltage)