A MAX232 will only give you about 10V out at the + end of C3, per the datasheet.
http://datasheets.maxim-ic.com/en/ds/MAX220-MAX249.pdfThe circuit above includes a 555 TIMER
INTEGRATED CIRCUIT, which is what was requested not used.
If the circuit is going to have an 8-pin IC anyhow, may as well make it a MAX734 or similar and
eliminate most of the other components.
http://www.maxim-ic.com/datasheet/index.mvp/id/1548A flyback circuit similar to this:
with the correct transformer could convert 5V to 12V with low parts count.
If noise in the circuit is the issue with a switching converter, a charge pump might be quieter, the
MAX662A, again, an IC
, might do the job.
Perhaps QTY 8 AAA alkaline batteries could to the job, they'd last quite admirably for such low-current intermittent use.