Ruby knight vindicator from Tome of Battle seems like your best bet. Crusaders make the best combat-healers in the game, and by going, say, Paladin 4/Crusader 1/Ruby Knight Vindicator 10, you get paladin spellcasting, crusader maneuvers, and a handful of other useful class features (including the excellent Divine Impetus). You don’t get to progress Smite Evil, and you don’t receive the special mount (and even if you delayed RKV by a level to get it, you wouldn’t progress it), but you still are a paladin, including Divine Grace, Lay on Hands, and Aura of Courage, and you progress paladin spells.
The Battle Blessing feat from Complete Champion allows you to cast your paladin spells as a swift action. This combines incredibly well with Divine Impetus. Sadly, mystic fire knight is out since it replaces Turn Undead, which you need for RKV and Divine Impetus: maybe your DM will let you replace something else? Or, if you can convince your DM to allow an adaptation of the mystic ranger from Dragon vol. 336, a “mystic paladin” option would be even better. Basically, the better your paladin spellcasting, the better this is going to work.
In fact, it may even be worthwhile to go for high Wisdom just for the spells, in which case Serenity from Dragon Compendium has a lot to offer. Alternatively, Dynamic Priest from Legends of the Twins (Dragonlance setting) makes your bonus spells and max spell level work off of Charisma; since your spells are unlikely to be forcing saves, that should work out well enough.
You may also be interested in the harmonic knight variant from Champions of Valor; it trades your at-will detect evil for Inspire Courage +1, once per day. That may fit your purpose better, and both the 1/day and the +1 can be boosted in a number of ways (e.g. Extra Music and badge of valor, Song of the Heart, and/or Words of Creation). Plus, Song of the White Raven allows you to start Inspire Courage as a swift action, and you’ll get plenty of those.
Now, ruby knight vindicators are required to worship Wee Jas, and gain two features that reflect that worship: access to Shadow Hand maneuvers, and the Armored Stealth feature. These could easily be fine for you, and make for an interesting take on a healer. On the other hand, they’re definitely not typical healer-y things. You could just ignore them, by not selecting any Shadow Hand maneuvers and by just not training Hide/Move Silently/Stealth; without ranks, losing the armor check penalty to these skills isn’t going to make you especially great at it.
However, there is also this this solid homebrew effort that defines alternate vindicators that receive a different discipline and class feature to replace Armored Stealth. It does reference many homebrew disciplines (including one of my own, Chthonic Serpent), but the “burning light vindicator” of Pelor is notable for two things:
Its discipline is Desert Wind, rather than some homebrew your DM would have to vet separately; you probably won’t actually bother to use much of it, but it does stand a good chance of being far more appropriate than Shadow Hand.
It gets raise dead as a spell-like ability once per day. This means that it has no material components, so it costs you nothing to use (it still costs the target a level, of course). This is relatively high-power, but that is intentional since Shadow Hand is one of, if not the, best disciplines, and Desert Wind is the worst.
After the vindicator, adding more spells to your spell list is very desirable here; this interacts well with Battle Blessing. Domains are one of the best ways to augment a spell list; per Complete Divine, non-clerics simply add the spells to their own lists, though they can each only be prepared once a day. And even if you have to worship, say, Pelor, and thus are often limited to his domains, Heretic of the Faith from Power of Faerûn can allow you to take some other domain (it also eases your Code of Conduct). And there are a lot of ways to get domains:
A domain icon from Faiths of Eberron allows you to spontaneously cast the spells from a single, specific domain, even if you don’t have that domain, as long as you worship the god that the icon is associated with (obviously, the icon can only be attuned to domains that god offers). You’re explicitly swapping a spell you prepared for this spell and casting it yourself, so it should qualify as a paladin spell and thus for Battle Blessing. This only works three times per day, but then you can just buy more copies of the same icon.
Note that Domain Spontaneity from Complete Divine is this in feat form, for a single chosen domain that “you have access to.” A feat costs more than an icon, by quite a bit, plus you need to already have the domain, but depending on your DM and the campaign, the feat may be more reliable. It also burns Turn Undead uses, which can be a good thing (you should have way more of those, compared to the domain icon’s 3/day limit), but comes at a cost (you want Turn Undead uses for Divine Impetus).
The contemplative from Complete Divine adds one domain at 1st and another at 6th. It’s also dead-simple to enter and full-casting. The Healing domain is an obvious choice, though a somewhat-disappointing one: all it really does is let you use cure moderate wounds and cure serious wounds as spells of the correct level (but still much later than a cleric), and you get to add cure critical wounds to your repertoire. None of these is a particularly good spell, though.
A healing domain icon is the better approach for these. The granted power of the Healing domain is worthless except on heal, which is very difficult to cast as a paladin.
Instead, a domain that grants a powerful granted ability is more desirable. There are many, many options for that, and if you can convince your DM, you may also have the option of swapping that domain for the corresponding devotion feat from Complete Champion (though by default, if I recall correctly, that option is only available to clerics).
An alternative use for the domain from contemplative would be the Sun domain and thus entry into radiant servant of Pelor, though I don’t think the class is all that good. Supreme Healing sounds impressive, but Empower and Maximize do very little to cure spells because they use relatively few dice. By far the best spell on the Healing domain, heal, doesn’t benefit at all from either, but you couldn’t cast that as a paladin anyway.
Worse, Maximize Healing is effectively available by simply taking Maximize Spell and then Mastery of Day and Night from Player’s Guide to Eberron – you get to automatically maximize cure (and inflict) spells, which covers everything in the Healing domain that you could actually cast anyway (and only regenerate misses out, if you somehow managed to get it).
If you can convince your DM to allow the radiant servant features to apply to Devoted Spirit maneuvers (crusader’s strike, revitalizing strike, rallying strike, and strike of righteous vitality), that would make RSoP (or Mastery of Day and Night) somewhat more worthwhile. These maneuvers are each very close to various Healing-domain spells (rallying strike is closer to mass cure serious wounds than the mass cure critical wounds in the domain, but mass cure critical wounds is the better spell anyway). Unfortunately, the one maneuver that actually explicitly gives the benefit of a Healing domain spell “as cast by a cleric of your level,” strike of righteous vitality, is giving the benefit of heal, which doesn’t benefit from radiant servant to begin with.
The church inquisitor, another Complete Divine prestige class, adds the Inquisition domain and its rather-nice +4 bonus on dispel checks at 1st, and is full-casting. The 2nd level grants immunity to charms, which if combined with any of the protection from alignment spells, is fairly thorough protection against a lot of the worst enchantments.
The divine oracle, also from Complete Divine, adds the Oracle domain at 1st. It also adds a pretty sweet Evasion-in-any-armor at 2nd, and is full-casting.
The sovereign speaker from Faiths of Eberron adds nine domains over as many levels, though it loses two spellcasting levels along the way. This one does require worship of the Sovereign Host pantheon, which conflicts with both Wee Jas and Pelor, and isn’t covered by the linked thread, but if playing in Eberron some adaptation is necessary anyway.
But do note that after Paladin 4/Crusader 1/Ruby Knight Vindicator 10, your initiator level is 13th, and you really want it to hit 17th for strike of righteous vitality, which is easily the best single-target healing option in the game (and were it not for mass heal, would otherwise easily be the best healing ability in the game, full stop). That means of the five remaining levels, you need to gain 4 initiator levels: only two of those five levels can be in non-initiating classes if you are going to do that. You also need to ensure that you’re actually entitled to select a maneuver once you hit 17th.
This works out OK, though, because you have the spellcasting of a 12th-level paladin; you only need two more spellcasting levels to hit 14th and get 4th-level spells. So by taking two spellcasting levels and three initiating levels, you get 4th-level paladin spells and strike of righteous vitality. That’s a big win.
Finally, this homebrew knight-protector I made may be a good choice for you, though it focuses much more on the crusader aspects and advances nothing from paladin. Still, a mix of paladin, crusader, vindicator, and knight-protector could work quite well for your goals.
My preference, I think, would be as follows:
Paladin 4th, with Harmonic Knight variant, and either Dynamic Priest or Serenity as befits the character. Extra Music if I could fit it.
Crusader 1st, making sure to pick up mountain hammer and at least one White Raven maneuver to qualify for Song of the White Raven. The level stacking doesn’t help, but starting Inspire Courage as a swift action is worth a feat anyway.
Burning Light Vindicator 7th, to get Divine Impetus ASAP, with a focus on Devoted Spirit and (maybe) White Raven.
Knight-Protector 3rd, to get Restorative Strike and the necessary initiator level.
Burning Light Vindicator to 9th, saving that last level for 20th ECL to take strike of righteous vitality.
Contemplative 1st; not sure on the domain yet.
something that progresses paladin spellcasting for a level, possibly just the 5th level of paladin.
Burning Knight Vindicator to 10th, gaining strike of righteous vitality and 4th-level paladin spells.
