There's some description of the very limited historical records in Morocco on Geneawiki (in French). May be out of date by now, and as it's a French site it makes no mention of the former Spanish areas.
In short: before 1912, few records, except consular records from their home country for Europeans.
1912-1956, records are in France. France Diplomatie (in French) has listings of some microfilms, but nothing is online. It appears none of the data they list there is recent enough for you, but you could contact them to see if more recent état civil (birth certificates) are available.
From 1956, you need to contact the specific commune (local authority) in Morocco (plus consular records are still useful for Europeans).
There is also the Association Généalogie Algérie Maroc Tunisie (in French) who may have access to other records.