The same way you deal with any team with a sustain advantage: focus on pushing. It's pointless to focus abilities on harassing the enemy team when Sona (or any healer) can just negate any damage you manage to land. Instead, concentrate on clearing the minion wave. (Easier said that done sometimes, depending on team composition.) But that's what you do -- do your best to shove the enemy team to their turret and siege away.
If your team has poor wave-clear -- or the enemy team has superior wave-clear -- ask, cajole, beg, or demand that your melee champions buy a Targon's Brace (or a Runic Shield, at the very least). That item alone puts melee-heavy teams on equal footing with AOE/pusher ranged champions. Recognizing how amazing Targon's Brace is for melee champions is something that differentiates the ARAM Bronze tier from the ARAM Gold+ tiers.