When R2-D2 and BB-8 converse in The Force Awakens for example, is there any written record of what the two characters were saying to each other?
I mean actual dialog, if it exists, and not something like ”BB-8 beeps excitedly”.
Nope. In the script it's all "BB-8 Beeps excitedly" and "BB-8 Bleeps mournfully", and so on. As far as his 'conversation' with R2-D2 is concerned, this is what you get:
LOW WITH BB-8 as he rolls over and finds, under a dark and dusty tarp in a corner, R2-D2. BB-8 BEEPS at R2, pulls off the tarp and tries to start a conversation. But R2 DOESN'T RESPOND AT ALL. BB-8 tries again. Nothing. BB-8 NUDGES R2. Nothing.
As BB-8 approaches R2-D2, the long dormant droid suddenly stirs. The droids beep at each other.