TL;DNR: If you have a safety problem climbing with children, it won't be because the rope is a bit old.
You need to define what you mean by 'Safely'. I put it that is impossible as it varies for everyone on a daily basis. This makes it one of those unanswerable questions.
However, if you rephrase the question - move the focus from just the rope - "Is a retired rope safe" to taking kids climbing as a whole- 'How much does using a retired rope increase the danger of taking children climbing' you get to question that has a useful answer.
The other answers focus on the safety of a retired rope. The difference in safety between a brand new rope and retired rope (as in 'recently retired because of standards and manufacturer recommendations' rather than damaged or had a big fall) appears small and insignificant compared to the other dangers.
So, given the dangers of climbing, I suggest using a retired rope is extremely unlikely to create or contribute to an adverse outcome for any climber, and significantly less so for child or top roped climbers. What this means for Top roped and children can only become insignificant.
All of the above being said, there is another aspect at play that will override all this common sense. If you do take children climbing on say a 30 year old rope, what will people think and say of you? Will you be treated as a cautious climber who has thought through the implications and understands and manages the risks very well, or will you be labeled an irresponsible cowboy idiot who should not be allowed near children. If you had an accident, say a child unties his harness half way up the climb for a laugh, the 30 year old rope would be used to hang you, no matter how irrelevant it was to the situation.