Hosting an exchange student is great! My husband and I have hosted 5 and are absolutely addicted to it! I am also a volunteer with Youth For Understanding (YFU), one of the oldest, largest, and most respected exchange programs.
I would like to submit a vote for hosting with YFU. Every year YFU brings approximately 2000 students to the USA. There are about 1400 volunteers (like myself) to help with any issues that arise and to conduct 'orientations' to help the host families and students to adjust. Additionally, each "Field" (45-70 exchange students per field) has a full-time paid Field Director. There are also Support Services Managers and counselors.
Hosting an exchange student costs very little - there are no 'sign-up' fees or anything like that. Financially speaking, all the host family is required to provide is room and board. The student may share a room with a host sibling of the same sex (preferably with one that is close in age) as long as they have a space to put their own belongs. The required 'board' consists of 3 meals a day and a few personal care items (can be limited to just toilet paper and hot water for showers). It is perfectly acceptable to require the student to make their own breakfast (all 5 of our kids have - I'm not exactly a 'morning person'). Lunches can be food provided from home, a school lunch ticket, cash in the amount of the school lunch cost, etc. None of the meals are expected to be fancy. The host family is not expected to provide meals out unless that is a family custom. (For example, if the entire family goes out to eat, the family pays; if the student goes somewhere on their own or with friends, the student pays.)
The chief expectation of host families is to treat the student as if he/she was a member of their own family. Some examples are: The family should assign the student a household chore. The family should help a little with homework (for example, explaining what a Governor is and how that differs from being a Senator) but should not give up their entire life to help. If it is family custom, the host parent(s) should give the student a goodnight hug. Appropriate consequences should be assigned for the student breaking a family rule (for example, if the student has trouble getting home by curfew time, they can be required to call 10-15 minutes before the curfew has expired).
Host families do have to undergo a screening process, but as long as no one in the family has any serious legal problems (eg convicted of murder) and your house is sufficient (eg keeps the snow off of you in the winter), there shouldn't be any problems.
I don't know if YFU has an office in Portugal or not, I will look into it. I know that students from Brazil come to the USA every year. Most come in the spring (their fall). If your cousin were to sign up with YFU, he/she could request a direct placement with you. As long as you pass the Criminal Background Check and your school will accept your cousin, I see no reason why he/she couldn't live with you.
This year has been particularly hard to find host families because of the economy and health scares (all exchange students will be of good health). Forgive me for being forward, but would you consider hosting a student this spring?
Check out the website and videos. If you email me, I can send you some .pdf files that include a question and answer sheet. If you live in Colorado or Wyoming, I can put you in touch with the nearest local YFU rep who will answer questions.
I wish you well.