I have had excellent results with the local archives for 1860's-1890's. Relatives were Roman Catholic and obtained marrige dates and birth dates last week. Address is:
Primaria Orasului Anina
Str. Sfanta Varuara NR.49
If you have the local Catholic Parish address could you post?
I wrote in English and enclosed $5.00 for each request. Reply in Romanian, But easy to decipher.
Hope this helps.