chemistry

Your net ionic equation is correct. Good work. However, I think the problem is a little misleading since the net ionic equation doesn't have a conjugate base for the acid. If you write
H^+ + CO3^2- ==> HCO3^- as the net ionic equation, which I believe is correct, then the CO3^2- is the base and HCO3^- is the conjugate acid. Then H^+ is the acid but no conjugate base is shown because the NO3^- cancels when the net ionic equation is written. If you write HNO3 + CO3^2- ==> HCO3^- + NO3^- then HNO3 is the acid with NO3^- as its conjugate base while CO3^2- is the base with HCO3^- as the conjugate acid. I hope this makes sense. The main reason I think the problem is misleading is because it asks for the net ionic pairs yet the ionic part of the conjugate base (nitrate) cancels when one writes the net ionic equation. Technically I don't think that part has an answer.

Net ionic equation: H3O+(aq) + CO3^2-(aq) <--> HCO3-(aq) + H2O(l)
Acid: H3O+
Base: CO3^2-
Conjugate Acid: HCO3-
Conjugate Base: H2O

The hydrogen ion (H+) doesn't exist on its own in aqueous solutions because it's attracted to the unshared oxygen electrons in water. This forms hydronium (H3O+) ions, which are more stable.
Water is amphiprotic/amphoteric which means it can act as either acid or base. In this case, we need it to act as the missing base and to balance the net equation.
Please do not ask me why this is the answer, I have no clue, and what's above is just how I made it make sense for me.