There are several contenders for the name of 'ever spring country', but the most likely is the county of Chabahar, part of Sistan and Baluchestan Province, in the south-east of Iran.
Chabahar is also the name of the capital city of the province, a port city and free trade zone. The name 'Chabahar' comes from the Persian 'char' ('four') and 'bahar' ('spring', as in the season). This refers to the climate of the area, said to be like spring all year round. Chabahar also has springs in another sense - mud springs, caused by seismic activity.
Other Possible 'Ever Spring Countries'
Jamaica was so named by the indigenous peoples who lived there before the island was colonized, such as the Arawak tribe. They called the island 'Xaymaca' or 'land of springs'.
Guatemala takes its name from an ancient tribal word, 'Uhatzmalha', which translates roughly as 'mountain where water gushes'. However, this is only one theory of several as to how the country gained its name.
Finally, there is an 'Everspring Farm', south of Rochester, New York State, USA. There are so many towns, cities and geographical features starting with the words 'spring' in the USA, perhaps we could also call America 'land of the springs'.
Chabahar in Iran is famous for its exotic wildlife and beautiful landscape, as you can see in this YouTube film: