I was asked last week if one may serve their children Kneidelach this past Friday afternoon.
First of all, while the Mishna Berura writes that even young children should not be fed Fleishigs during the 9 days; the Magen Avraham permits it until the age of 9, and the Chayei Adam is lenient until Bar Mitzva.
Secondly, the Kneidelach are not actually made with Fleishigs and do not create the Simcha associated with meat which is inappropriate during this period of the year. Furthermore, it is even conceivable that the other ingredients are 60x the chicken in the soup.
Additionally, Rav Moshe Feinstein zatzal allowed that if this serves as their Shabbos Seuda and they will be going to sleep before the family reaches the Seuda, it would be permitted.
Finally, while its applicability to this case is questionable, the Poskim do cite a Mitzva to taste the Shabbos food on Erev Shabbos. If we could consider this a Mitzva, it may be permitted for this reason as well.
In conclusion, for younger children there are certainly grounds for leniency, especially if this is their sole Friday night Seuda.