Divine power is your only option
Divine power allows you to get BAB equal to your character level (not caster level, which is relevant if you have caster level boosts). It is only rounds/level, and it only appears on the cleric and war domain spell lists.
Clerics can easily make divine power last all day
The feat Divine Metamagic (Complete Divine) allows you to burn Turn (Rebuke) Undead uses in order to power metamagic applied to your divine spells, at a rate of one use of Turn (Rebuke) Undead per spell level increase the metamagic would have required. The Persistent Spell metamagic feat (Complete Arcane) gives a spell a 24-hour duration, and adds six levels to a spell. Combine the two, and you need 6 uses of Turn (Rebuke) Undead to use it. That’s either Cha 16, or Cha 10 and the Extra Turning feat (which can be gotten as the granted ability of the undeath domain (Spell Compendium). Persistent Spell itself requires Extend Spell, which again can be gotten as the granted power of the planning domain (Spell Compendium).
Non-clerics have a much harder time
If you are not a cleric, getting the spell on your own list can be pretty easy: you just need the war domain. Getting it to last is much, much harder: you still probably want to use Divine Metamagic, but you have to jump through hoops to get Turn (Rebuke) Undead and, if you’re arcane, to cast the spell as divine so you can use DMM.
Other divine spellcasters
The Contemplative prestige class (Complete Divine) is easy-to-enter for a 10th-level divine spellcaster, and grants one domain of your choice at 1st level. Pick the war domain.
The Sacred Exorcist prestige class (Complete Divine) grants Turn Undead at 1st level, and does not lose any spellcasting. You need to be able to cast dismissal or dispel evil though. Dispel evil is on the Good domain, if you can figure out how to get access to it. If nothing else, more levels in Contemplative will work, though that means you’ll be level 18 before you can get the combo together.
Otherwise, just take Extend Spell, Persistent Spell, and Divine Metamagic as feats. If necessary, Extra Turning too.
If you cast arcane spells, Arcane Disciple (Complete Divine) is the most straightforward way of getting divine power. Getting the spell to last is much harder.
Divine Metamagic is still the best way of accomplishing this. The problem is that it can only be used on divine spells. A dip in Cleric allows you to get Turn (Rebuke) Undead, Extend Spell, and Extra Turning, plus some divine spellcasting which qualifies you for Alternative Source Spell (Dragon vol. 325), which allows you to treat your arcane spells as divine (at the cost of −1 Caster Level, which doesn’t matter to persistent divine power).
Without dipping cleric, you need to get Turn (Rebuke) Undead; the only way to do that without losing spellcasting is the Sacred Exorcist prestige class (Complete Divine), and then you need to cast the spell as divine. Alternative Source Spell is still the solution to that, but to qualify you must first cast divine spells somehow. The answer to that is the Southern Magician feat (Races of Faerûn), but that may have undesirable roleplaying requirements (you must be a “Mulan human”) if you are playing Forgotten Realms, or simply be unavailable to you if not.
Without Dragon vol. 325 in play for Alternative Source Spell, your only option is doing something like Mystic Theurge so you can cast both arcane and divine spells. Note that Precocious Apprentice (Complete Arcane) can help you enter Mystic Theurge with minimal loss (i.e. as a Cleric 1/Wizard 3/Mystic Theurge 6 you can cast divine power and are only one level behind on your wizard spellcasting).
It’s usually better to just take high-BAB spellcasting prestige classes
There are a lot of them. Abjurant Champion (Complete Mage) is the best for arcane spells unless you’re a dwarf, in which case Runesmith (Races of Stone) is better (and as a dwarf you can totally take both; they’re each just 5 levels long). For divine, well as a cleric you should just use divine power and as a druid you should just use shapeshifting.