What I do to "simulate" firing arcs is to take the total 3-dimensional coverage of the ship's beam weapons (360 degrees horizontal + 360 degrees vertical) and give the ship one Coda phaser array per 720 degrees (or fraction thereof).
To simulate the FASA coverage is to look at how FASA works its arcs. forward and aft arcs are effectively 1/6 (60 degrees) of the horizontal coverage. The port and starboard arcs, however, are effectively 180 degrees horizontal.
Two combined arcs (f/p, f/s, a/p, a/s) cover 210 degrees horizontally. Three combined arcs (a/p/s, f/p/s) cover 330 degrees (since the only place a beam like that can't fire is directly fore or aft, respectively).
From there, I would look at where the actual bank sits in regards to the vertical arc. A phaser bank on the forward saucer hull (a la Constitution-class refit), would have vertical arc shadows at the edge of the saucer hull and at some point just above the bridge dome section. That's, roughly, a 135 degree arc.
So, taking that same weapon as an example, the Connie phasers are f/p, f and f/s, according to the Federation SRM. If memory serves, the pre-movie-era phasers were on the ventral saucer, which still provides for a 135 degree vertical arc.
So, the f/p and f/s banks would have a coverage of 345 degrees each, and the fwd bank would have a coverage of 195 degrees. That provides a total of 885 degrees...which I would convert to two beam weapon arrays in the Coda system.
Now, to be perfectly honest, I really didn't do that kind of work when I converted the FASA ships to Coda (see here). I simply divided the number phaser banks by two, and rounded up. I was doing a whole slew of them, so I was looking for some time savers.
But if you're wanting to go into that level of detail, I'd go with the method above. I hope this helps.
Davy Jones
"Frightened? My dear, you are looking at a man who has laughed in the face of death, sneered at doom, and chuckled at catastrophe! I was petrified."
-- The Wizard of Oz