Ok, let's see if i understand you correctly.
You, (the player) comes to 2 AI controlled Units (UnitA and UnitB) which are about to speak with each other. You as the player has nothing to do with (except following the convo).
As far as i know, you can do this with Gamelogics also with a script. Maybe you should give more info about what you already tried to do.
Also it would be helpful to know if you're only displaying text, or do you have sound files attached to it.
With Gamelogics you can do it basically very easy, as GL's can have waypoints which they'll follow.
So a way to do this could look like this:
Create a GL and assign some waypoints to it. Just ordinary "move" should work.
In the Init field of the first waypoint, insert a line which will let UnitA say his first part.
In the Init field of the second waypoint insert a line which will let UnitB say his reply.
and so on.
For the timings (as a gamelogic "walks" really fast from one WP to the next) use the timeout option into the waypoints.
To let the convo begin, just setup a switch trigger, which is synced with the GL's first waypoint.
All in all, this should work like an In-editor script...lol
Hope this helps you a step further