Children receive special attention in many of the post-conciliar rites. Four sections address the liturgical and pastoral situation of sick children.
47. What has already been said about visiting the sick and praying with them (see. no. 46) applies also in visits to a sick child. Every effort should be made to know the child and to accommodate the care in keeping with the age and comprehension of the child. In these circumstances the minister should also be particularly concerned to help the child’s family.
This is a sensitive area. Priests and ministers alike must be prepared for fruitful pastoral relationships not only with children, but adolescents too. How is a rite accommodated for not only the child but the family as well? Siblings of a seriously ill child would seem to require a particular pastoral care.
48. If it is appropriate, the priest may discuss with the parents the possibility of preparing and celebrating with the child the sacraments of initiation (baptism, confirmation, eucharist). The priest may baptize and confirm the child (see Rite of Confirmation, no. 7b). To complete the process of initiation, the child should also receive first communion. (If the child is a proper subject for confirmation, then he or she may receive first communion in accordance with the practice of theChurch.) There is no reason to delay this, especially if the illness is likely to be a long one.
Many pastors approach the parents with the possibility of completing Christian initiation. What circumstances might suggest this? Perhaps cancer at any age, any life-threatening hospitalization, any serious illness requiring several months’ absence from school. Any seriously ill child precocious enough to ask to be confirmed or receive the Eucharist would be a serious consideration.
Once initiated, frequent Communion:
49. Throughout the illness the minister should ensure that the child receives communion frequently, making whatever adaptations seem necessary in the rite for communion of the side (Chapter III).
And anointing, whether initiated fully or not:
50. The child maybe anointed if he or she has sufficient use of reason to be strengthened by the sacrament of anointing. The rites provided (Chapter IV) are to be used and adapted.
Catholic Sensibility 
One of the more intense moments of my priesthood was the emergency Christian initiation and anointing of a dying child in ICU. During the administration of the four sacraments the boy started to noticeably recover and eventually left the hospital healed.
There isn’t much “discussion” with the parents in cases like this. If a child is in danger of death, I simply inform the parents that the child is to receive all three sacraments of initiation (or two sacraments if the child is too young to receive the Host) as well as Anointing of the Sick (if of proper age). Never had any parents complain about that.