Good arguments? Heavens no.
They boil down to:
Clerics don't cast illusions!
Bards don't wear heavy armor!
Wouldn't a character that does both be cool?
Since arcane bards will have a slight edge in spellcasting due to their single stat dependency, I'd suppose that a lot of divine bards would make full use of their only other difference - freedom from arcane spell failure - by dipping in a class that gives heavy armor proficiency (putting their spellcasting further behind) or by taking the appropriate feats (also suboptimal), which would generally push them into a less roguish, more martial role, further from an arcane bard and closer to, yes, a cleric.
If a divine bard didn't dip for heavy armor, then the differences from an arcane counterpart would be mostly RP, but I see that as the same sort of problem/challenge as trying to, for example, distinguish two NG clerics with the Fire and Earth domains, one worshipping Chennet' and one Geoth - absolutely identical mechanics there, but probably very different end results.
If you want a divine caster (in heavy armor), why not just play a high Cha cleric? Well, bards have a completely different spell list, besides the other mechanical differences. You're trading 9th level cleric spell progression for spontaneous bardic spellcasting to 6th level (or possibly less good than that), supplemented by bardic music, and extra skill points wrt the cleric, or better BAB etc wrt the cloistered cleric.
Paladins are heavily armored half-casters, in that sense somewhat like a divine bard could be, but they come with their own enormous RP baggage, so let's ignore them as a general substitute.
I like the idea of a heavily armored guy brandishing his holy symbol and longsword, looking all for the (en)world like a paladin or cleric, then casting Mirror Image or Greater Invisibility (or Glitterdust, or Sleep, or Silent Image, or...)!
As for deities that might be patrons of divine bards, looking down the list, I can see a lot that would fit well: Phyrah as the most obvious, but also Galatea, Halina, Valessa, Zephos, Azwan, Verdante, Amphousa, Geoth, Grendath, Jareth, Taurusk, Ahrianna, Mongrel, and Ulura, at the least. Divine bards of some of these gods would be very restricted in alignment choices.
I, uh, don't think I'm going to spend any time right now attempting to create fluff for divine bards of specific traditions. Seems a little pointless for an unapproved class variant! If it passed, I'd contribute where I felt I had something to say, of course, but I'd rather leave a lot of it up to (a) anyone who has particularly proprietary feelings towards a deity, as well as (b) any eventual divine bard player. As usual, I'd not like to see anything too proscriptive: I'd not want someone who had a firm idea for a divine bard of Zephos as a Good (well, true neutral!) Shepherd-type figure (incidentally, you can't take two steps without tripping over medieval songs about shepherds! Hé, bergier! Pastorele, gente et bele!) to be told that it was out of the question, because his divine bards conduct funerary rites, or recite odes in memory of fallen heroes, for example.