Hi Bob,
Your question has no quick and easy answer. Consider this: If your battery is a good, solid voltage source with low source resistance, there is no need for a capacitor in parallel with it. Such a capacitor is usually added as a counter-measure to a weak battery condition. In this case, the battery impedance is relatively high. The capacitor provides a low source impedance for AC signals. A transient or AC load current is supplied by the capacitor. Without it, the battery voltage would waver in response to the varying load current. Even with it, the average voltage will sag--the capacitor cannot supply continuous current.
The need for a capacitor and choice of its value depend on the dynamic nature of the load current--how much does it change and at what frequency. The other factors are the maximum source impedance of the battery (weak battery condition) and the acceptable variation in battery voltage due to the AC load variation.
For a quick estimate, consider that if a constant load current must come solely from the capacitor. The voltage on the capacitor will sag at a rate of I/C volts/second.
In any event, you should at least have a capacitor to assure a low impedance at very high frequency to assure stability of the rail splitter and BUF634. I'd recommend a 10uF tantalum capacitor.
Regards, Bruce.