Ich antworte, ohne dabei der hierzulande rechtl. sehr engen Auslegung des Begriffs „sicherer Aufnahmestaat“ zu folgen:
Für Asyl gem. GFK käme bspw. vergleichsweise zuverlässig der Sudan in Frage. http://www.resettlement.eu/page/eritrean-refugees-eastern-sudan
Auch in Äthiopien gibt es UNHCR-Camps bspw. Hisats. http://www.unhcr.org/news/latest/2013/6/51b9b66b9/eritrean-refugees-ethiopia-new-camp-north-country.html
Eritrean refugees cross into Ethiopia through 16 entry points from which
they are collected and brought to a reception station for screening and
registration. Before departure from the reception centre, the refugees
are issued with basic assistance items, including sleeping mats,
blankets, jerry cans, water buckets, soap and mosquito nets. They are
also provided with tents and food rations once they get to the new camp.