A 15th level cleric has Divine Metamagic and can cast spells of 8th level, but not of 9th level. Can he spend two turn/rebuke undead attempts to heighten an 8th level spell to 9th level?
Yes, he can.
Compare the wording of Divine Metamagic:
As a free action, you can take the energy from turning or rebuking undead and use it to apply a metamagic feat to divine spells that you know. You must spend one turn or rebuke attempt, plus an additional attempt for each level increase in the metamagic feat you're using.
to the wording of Metamagic Song:
When you spontaneously cast an arcane spell that is enhanced by a metamagic feat, you can spend a number of uses of your bardic music ability equal to the number of extra levels that the metamagic feat imposes on the spell rather than raising the spell's effective level. Applying metamagic spontaneously using this method increases the casting time of the spell normally. You cannot use the Metamagic Song feat to add metamagic feats that would make the spell's effective level higher than the highest level of spell that you can cast normally.
Metamagic Song has the magic words that prevent this; Divine Metamagic does not. Likely, by the time they wrote Metamagic Song for Races of Stone, they had learned from their mistakes with Divine Metamagic in Complete Divine, since Divine Metamagic is one of the most powerful feats in the game (almost as instant-pick for clerics as Natural Spell is for druids). However, that’s purely speculative on my part, and for what it’s worth, they never issued an errata for Complete Divine saying that. Maybe they only put that limitation on Metamagic Song because Metamagic Song works on any metamagic you want to use, rather than working only on one particular thing you chose when taking Divine Metamagic.
Note that you can get around the limitation on Metamagic Song with Talfirian Song from Races of Faerûn, because of course you can.
Oh, and also, metamagic effects don’t “heighten” spells per se, unless you’re talking about Heighten Spell specifically. The word “heighten” refers to causing a spell to actually count as higher level, for the sake of things like DC, overcoming globe of invulnerability, and so on. Aside from Heighten Spell, metamagic effects don’t do that—they increase the spell slot used by the spell without actually changing the spell’s actual level for those purposes.