Strictly speaking, the only dictionary-defined reading of 永遠 is えいえん, but you might be noticing that in fiction and poetic writing, people will sometimes get creative with which words they assign to which kanji.
It's possible you might see the kanji written as 永遠 but pronounced as some other word with a similar meaning, like とわ or とこしえ, or even the English フォーエヴァー or something. The written kanji form allows them to solidify the meaning, but then the spoken word allows for a creative nuance to it, that may or may not be found in dictionaries.
Maybe you had some other example in mind though, so please share if that's the case.
Came across the とわ reading of 永遠 this week. Was so confused and frustrated because I could swear that the singer wasn't singing えいえん but it said 永遠 in even the official lyrics. Checking in the dictionary I couldn't find an alternative reading but after asking in the youtube comments section a bunch of Japanese speakers helped me out and explained that it could be read as とわ and you'd often hear it this way in songs. Was such a relief to find out because I was really starting to think I might need to get my hearing checked! Wish this reading was listed on jisho or that I'd at least seen this forum post before - it would have saved me quite the headache!
There are many similar questions found on Stack Exchange:
http://japanese.stackexchange.com/questions/tagged/creative-furigana
The とわ reading is listed among the forms on 永久 which appears to mean the same thing, second to last one:
Other forms: 永久 【とこしえ】、長しえ 【とこしえ】、常しえ 【とこしえ】、永え 【とこしえ】、永 【とこしえ】、永久 【とわ】、常 【とわ】
In case anyone is curious, the song I encountered the とわ reading in was Owaranai Melody wo Utaidashimashita (終わらないメロディーを 歌いだしました, ED from Sunday Without God).
永遠 pronounced differently than えいえん in music
Sometimes in music lyrics, I see 永遠 but it isn't said as えいえん. Can someone please help me with this? Are there other ways to say 永遠? I know 永 is なが and 遠 is とお.い, but because of the Japanese language, they change from onyomi to kunyomi.