Liberal:
It truly is amazing how rich and varied Southern accents are. There are even portions of the South (large portions) where the long “i” is not a diphthong at all. It’s a sound akin to “a” in cat, but a bit sharper, with a relaxed palate. Regarding Rubystreak’s example of “child”, it is once again the liquid consonant that is the problem. Both “l” and “r” come with initial sounds preceding them. It isn’t the “i”. Consider “vile” and “vale” and “veal”. They all get the schwa — vi-uhl, vey-uhl, vee-uhl.
I had a Texan linguistics professor who remarked once that “pie” is a pure vowel in Texan speech. I can make the sound, but it’s not one that exists in my native dialect at all.
Where I am, “fire” rhymes with “buyer”, “friar”, and “fryer”. As well as “wire”.