Hi,
I had similar problems with TRS/MAX3221 (it's the single channel version of MAX232).
The charge pump was the problem. This particular type has a two stage arrangement, the first stage boosts up the Vcc to 5.5V, and the second stage inverts it to -5.5V.
The first stage is a simple charge pump booster, and that's where the problem was coming from. This booster stage is a fixed frequency, fixed (50%) duty cycle, burst mode converter. It means it runs in bursts to recharge the cap the at V+.
At my design, the burst were short with long intermittent waiting time, but during such a burst, the IC took over 100mA (if I remember correctly). These powerful burst load caused ringing in the supply lines.
I figured, that if I slow down the charging of the flying cap, I will have longer bursts and shorter waiting times, but with proportionally lower input current amplitude. I simply added a 47 ohm resistor in series with C1.
I checked however, if the IC can output enough power to drive a worst case load on the RS232 TX line, with the lowest Vcc that can occur. I found that even this load was not so severe to make the burst/waiting time ratio more than 70-80%. (I deliberately didn't use "burst duty cycle" to avoid confusing it with the charge pump's fixed 50% duty cycle).
Even with this trick I didn't fully succeed. I needed to increase the Vcc decoupling to 4.7uF and place a 22ohm resistor in series toward the rest of the power line.
Good luck, pls. report if it works for MAX232 too.
Gabor