Suppose there existed a spell with Convoke that also had an additional cost of untapping one or more tapped creatures you control. For this example:

Major Weirding
Sorcery
As an additional cost to cast Major Weirding, untap a tapped creature you control.
Target player discards a card and loses 1 life.
Convoke

If I control a single black creature, could this spell be paid for using only that creature?

The Comp Rules has this to say about paying costs:



It doesn't really truly go into detail about what that means. I mean, partial payment seems to mean you can't cast the spell by paying only part of the total cost. But what about the payment order? Like, do I have to pay all mana at once, or could I pay , then untap a creature, then pay ? And if I could do that, what stops me from instead tapping my black creature to pay for through convoke, untapping that creature through the cost, and then tapping it again to pay for ? The total cost has been paid, and in an order of my choosing.

Think of this as more of a question exploring whether something is capable of being done with Convoke and trying to figure out how disastrous such a spell could be (and thus whether it should be avoided entirely or come with very steep costs).

The sentence "Partial payments are not allowed," means you are not allowed jump around between various parts of the cost, making weird incomplete payments on each component, promising that when you are all done everything will be paid, cross-your-heart-and-hope-to-die. Instead, the cost is partitioned out into its components (mana, additional cost action A, additional cost action B, etc.), those components are ordered however you choose, then complete payment is made on each component before moving onto the next component.

So the answer to your question is no. When you attempt to pay the mana component of the cost, you will have one untapped creature to pay for one mana of the cost. The other mana must come from somewhere else. (Strictly speaking, if we reach this point, you probably did not activate a mana ability for that second mana; hence, you would not be able to pay the costs for the spell and the entire casting would be rewound.) Only after you have paid all of the mana may you move on to untapping a tapped creature you control.

ADDENDUM: If you had a second already tapped creature you would be able to cast that spell without paying any mana because you would be able to take the "untap a tapped creature" action before the mana payment. Then, when you began the mana payment, you would have two untapped creatures to pay for the full mana payment.