One way of handling this situation is to create characters as a group. Rather than coming to the table with your sheets already made, take a session and built the team together. It's easier to encourage diversity at the concept stage than to tell someone with a built PC that they have to start from scratch. Moreover, you can be there to ask questions like, "You've all built mages with one street sam — is he the bodyguard?" or "Your only source of magical healing is the paladin; does anyone want to roll a cleric or warlord?"

The Healing Light feature gives you a bonus action which basically replaces the Healing Word spell — which you don't get.

You're going to be leaning heavily on that, because your selection of healing spells is limited — the warlock doesn't have any on its normal list (except some necromancy stuff, which only heals you), so all you have are those from the Celestial Expanded Spells feature: Cure Wounds, Revivify, and Lesser and Greater Restoration.

At 6th level, it is probably going to be fine. You're missing the "big guns" like Mass Cure Wounds and Heal, but those aren't available to anyone at this level. And fortunately, you've got bards for the Song of Rest, so your party has short-rest healing benefits available.

I don't think you need to do anything particularly special to "build" this — just avoid focusing on other things that will consume your bonus action for Healing Light. You could look at the Healer feat, but in most cases going for straight Charisma boost is going to do more — it increases the number of dice you can spend at once on Healing Light, and significantly improves all of your non-healing stuff, while the feat just gives you a weak alternative to the Cure Wounds spell you already have. The Acolyte background would give you story-based access to temple services, which might be handy depending on the game and setting ­— but it sounds like you already have a background in mind.

For a Charisma-based divine caster, you may look instead at the Divine Soul sorcerer — you could generally flavor this to fit many similar story ideas, and you'd have access to the full cleric spell list (and twinned Healing Word is awesome).