Can I use MAX232 instead of a ICL7660 to make a split power supply?
A charge pump can be appropriate for making power supplies for low-power opamps.  A MAX232 contains two charge pump supplies, which can be used for your purpose, maybe.

The MAX232 will create a positive and negative voltage, but since those supplies are designed to power its internal circuitry, extra available current will be limited.  If you don't load the RS-232 lines of the MAX232, then it should in theory have some excess current capacity you can use.

Check the datasheet to see if there is any spec on how much current the charge pumps generate and what, if any, is left over for the external circuit to use.  You are probably on thin ice spec-wise, since the MAX232 isn't intended for how you plan to use it.  You can probably get some guidance on the current capacity by looking at the maximum current the MAX232 can source and sink from/to the RS-232 lines.  Then leave those lines unconnected and assume that the extra current is probably available for you to use.

However, dedicated charge pump chips are available and no more expensive than MAX232, so it makes more sense to use one.  They will then come with proper specs so that you can know up front whether your design is violating maximum capability or not.

Regardless of whether you use a MAX232 or a dedicated charge pump chip to make your opamp power supplies, be sure to put a little filtering between the supply and the opamp.  A ferrite "chip inductor" followed by 20 &micro;F or so cap to ground on each power feed of each opamp would be a good idea.  That kills the high frequency noise from the supply, leaving the lower frequency variations that the active circuit in the opamp should be able to deal with.