I think that indeed the old marriage rules have been applied for the last time in 1966, when Prince Albrecht von und zu Liechtenstein married morganatically to Tamara Nyman, who was created Baroness von Landskron, and their children bore their mother's title.
In the same period, however, some marriages of Princes von und zu Liechtenstein to women born into minor noble families were considered as equal (i.e. the marriage in 1969 of Prince Franz to Laura Malvezzi Campeggi, who was the daughter of an Italian Marquess).
However, by the early 1970s also the marriages of the members of the Princely Family to commoners were regarded as equal and no longer as morganatic; the most emblematic case IMO is the marriage of Prince Philipp (a brother of Fürst Hans Adam II) to Isabelle de l'Arbre de Malander in 1971.
I don't know if the new rules about marriages were written in some document or something similar. However, the 1993 Constitution of the Princely House
lists the current rules about marriages of the members of the Princely House.
Basically the Constitution says that:
1) When a member of the Princely House has the intention to marry, he must inform the Reigning Prince about it and deposit a series of documents required by the Constitution itself and by the law to the secretariat of the Reigning Prince. If the documents are complete and the Reigning Prince considers that all conditions for approval of the intended marriage are met, then the Reignign Prince will declare his consent to the marriage. The Reigning Prince shall then notify his decision to all the members of the Princely House who are of full age.
2) Within one month by the time of the notification of the Reigning Prince's consent, any member of the Princely House who is of full age may object to the intended marriage. The Reigning Prince shall then inform the Family Council of the objection and he will then decide on the objection.
3) If no objection is raised or if the objections are rejected by the Reigning Prince, the intended marriage will be publibly announced and shall then take place within one year.