Not in the same action

Attacking a creature is an Action. Bestow curse, the example you linked, also requires an Action to cast. Your character cannot do both at once.¹

This is a matter of adhering to the action economy in this edition of the game.

As flavour

Absolutely! If you have haste, or spread it out over two turns and it makes sense, casting a spell through teeth sunk into flesh is a really fun idea! A spell with touch range and no melee attack is effectively a spell with 5ft range (on a grid). All you need to do to cast the spell is to be adjacent.

¹_{If you had multiclassed as a Fighter, and have the Action Surge feature, you could take two Actions in the same round.}

Yes, you can

On Holding the Charge, it says:

If you don’t discharge the spell in the round when you cast the spell, you can hold the discharge of the spell (hold the charge) indefinitely. You can continue to make touch attacks round after round. You can touch one friend as a standard action or up to six friends as a full-round action. If you touch anything or anyone while holding a charge, even unintentionally, the spell discharges. If you cast another spell, the touch spell dissipates.

Alternatively, you may make a normal unarmed attack (or an attack with a natural weapon) while holding a charge. In this case, you aren’t considered armed and you provoke attacks of opportunity as normal for the attack. (If your unarmed attack or natural weapon attack doesn’t provoke attacks of opportunity, neither does this attack.) If the attack hits, you deal normal damage for your unarmed attack or natural weapon and the spell discharges. If the attack misses, you are still holding the charge.

This means that instead of trying to touch your target with a standard action, you could use a full-round action (such as Flurry of Blows or a Full Attack) and attempt to deliver a held charge on each of your unarmed attacks. Keeping in mind that each attack will provoke attacks of opportunity unless you have the proper abilities to prevent those (like Improved Unarmed Strike or similar).

The wording on Darkfire is very similar to Chill Touch, or even Produce Flame, which are common spells to use like this.

Darkfire

Beginning the following round, you can strike opponents with a melee touch attack, dealing 1d6 points of damage per 2 caster levels (maximum 5d6. Alternatively, you can hurl the flames up to 120 feet as a thrown weapon. When doing so, you make a ranged touch attack (with no range penalty) and deal the same damage as with the melee attack. No sooner do you hurl the flames than a new set appears in your hand.

Produce Flame

You can strike an opponent with a melee touch attack, dealing fire damage equal to 1d6 +1 point per caster level (maximum +5). Alternatively, you can hurl the flames up to 120 feet as a thrown weapon. When doing so, you attack with a ranged touch attack (with no range penalty) and deal the same damage as with the melee attack. No sooner do you hurl the flames than a new set appears in your hand.