I have never heard of hostels (called "hostales" in Spanish) specifically for
married couples but most are built with the couple in mind - married or not. Well.. hmmm.. that is to say, that TWO people will be staying in the rooms. However, many many (or most) hostels offer rooms with TWO single beds so the couple would not (necessarily) be able to sleep in the same bed. If you're looking for a double bed or ONE bed for two persons ask/look for a "cama de matrimonio" & read the insightful "
Double bed vs. Twin bed " thread for more details.
You can distinguish hostels (called "hostales" in Spanish) from YOUTH-hostels (called "albergues juveniles") by the fact that youth-hostels almost always only have dorm-style or boarding-house style lodgings with many many bunk-beds in each room, community showers and bathrooms, etcetera. We English-speakers somehow, along the road, abbreviated "youth-hostels" to "hostels" which does a disservice to the Spanish language when referring to inexpensive lodgings. If you ask a Spaniard in English to tell you where is the nearest "hostel" he'll direct you to a "hostal" and not to a "albergue juvenile".
Hostels, on the other hand, give their guests individual rooms, often in-room bathrooms/showers, their own key, possibly their own balcony, and 24-hour access to the building.
There are dozens upon dozens of hostels reviewed here in this category so be sure to do a search or browse the last 60 days of postings for Madrid hostels. You'll no doubt come across reviews for Hostal Adriano, Hostal Chelo, Hostal López, Hostal Bianco II, and many many others.
If you're looking for somewhat more expensive hotels (but still relatively cheap as compared with other hotels in Madrid) be sure to consider Hotel Plaza Mayor and Hotel Europa on the Puerta del Sol.
Anyone have specific suggestions/recommendations?
Saludos, MadridMan