Is it permissible for children to falsely swear that they saw a person delivering the signed contract to their father, in order to avert the charge of forgery and imprisonment from him, knowing that they did not see that?

If the father is to be unjustly imprisoned due to a forgery against him, and you are certain of his innocence, then it is permissible for you to swear falsely to save him. If it is possible to use tawriyah (ambiguity/double meaning) in the oath, then outright lying is not permissible. If it is not possible, then there is no impediment to swearing falsely for this purpose, as lying may be permissible or obligatory in certain circumstances. Whenever ma'areed (euphemisms/indirect speech) can be used, outright lying is forbidden. If the matter requires an oath to save an innocent person from destruction, then one must swear it.