if the father is blood type AB and the mother is blood type O, what blood type would indicate that their?

Depends whether or not their blood group is rhesus neg or pos..

If the child has type O blood, then he/she is adopted!  A father with type AB blood and a mother with type O blood can only produce offspring with either type A or type B blood.  In order for one to have type O blood, they must inherit two copies of the recessive type O allele, one from each parent.

Edit: I forgot to add, that if the child has type AB blood, then he/she is also adopted, as A and B are the only possible blood types.

Generally type AB or type O.
Things get more complicated if alleles for Bombay phenotype are present in this family.

Things get simpler if you just ask Mom, "Say, how was your hospital stay when you were giving birth to Junior?"

We each have two of the alleles A, B and O (we can have any two, including two of the same) but we only pass on one of them to our offspring. Someone with AB blood has an A allele and a B allele. A and B are dominant over O (so if you have either of them and an O, you won't be blood type O) so the only way for the mother to be O is to have two O alleles.

This means that the father can pass on either A or B and nothing else. It also means that the mother can pass only pass on O. Since A and B are dominant over O, the child will either have A or B blood type: A if the father passes on A, and B if he passes on B.

Since the child can only have A or B blood, they're probably adopted if they have AB or O blood.