There are two ways of writing 朋友 for the simple reason that there are more than one way to pronounce the word. In mainland China, the standard is with a neutral tone, so péngyou (现代汉语词典，第7版).
However, as is often the case, it can also be okay to pronounce the word with a full tone on the second syllable. For example, the standard in Taiwan is with a third tone, so péngyǒu (國語辭典). Please note that this may or may not reflect how actual people talk, and you'll find variations across regions, age groups and so on.
For communicative purposes, it doesn't matter which of these you use since the risk of being misunderstood is insignificant.