Say the parents are close friends with other Korean parents. They all have their own kids. The kids hang out together and are close friends as well. Now, how would a Korean kid address his/her own parent's friend (male/female)?
아저씨 (male) and 아줌마 (female) may be used if the kid really has to use an address word, but neither of them sounds very nice or inviting (아저씨 and 아줌마 are more for strangers or sometimes for certain types of relatives than close friends of the family).
If there is a need, the parents might tell the kid how to call their friend, and in this case they might use the friend's last name with 선생님 (e.g. 박 선생님), which is more common for male but applicable to female too. Alternatively they might use a place name (where they come from) like 부산 아저씨, 청운동 아줌마, 광주 선생님, etc.
But I believe none of the above are very common because kids actively interacting with parents' friend is uncommon.