On the same Unsolved Mysteries forum I linked to which discussed the lost prototype of UM called "Missing...Have You Seen This Person?", one user mentioned possibly still having a copy of a late 1980s special called "America's Search for Missing Children". It was hosted by Shirley Jones of Partridge Family fame.
The exact year is unknown, but it had to have aired sometime after April 1988 as one missing child featured (Michael Henley) disappeared on April 21 of that year. Henley was also featured on UM on September 20, 1989. His remains were found in 1990 and it was ruled an accidental death due to exposure when he wandered away from his family's campsite.
There's really no info I can find about this special outside of that thread. There's not even an IMDB page for it.
I am not by any means an expert in this area but take a look at the linked video below starting at: 14:20. This show was mentioned in the 1989 48 Hours Special "Trash TV".