It is not permitted. In a letter dated September 1, 2008, the Congregation for Divine Worship and the Discipline of the Sacraments issued the following directive: “This Dicastery observes that Canon 1003.1 expressly forbids anyone, other than a priest, to administer the Sacrament of the Anointing of the Sick. Furthermore…, no other person than a priest may act as ordinary or extraordinary minister of the Sacrament of Anointing since such constitutes simulation of the sacrament. This Congregation also observes that there are only three blessed oils used in the Roman Ritual namely, the Oil of Catechumens, the Oil of the Sick, and the Sacred Chrism. The use of any other oil or any other “anointing” than those found in the approved liturgical books must be considered proscribed and subject to ecclesiastical penalties (cf. canons 1379 and 1384)” (Prot. 824/08/L).
Even if well intentioned, such anointings cause confusion and are difficult to distinguish between the very similar looking Sacrament of the Anointing of the Sick.
One might certainly pray for the sick, and even lay hands on them. But anointing them with oil is going too far, for the reasons stated.
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