The final sound in "day" is called a diphthong. A diphthong (pronounced dif'thong, not dip'thong) is made up of two sounds: one sound is always a vowel, and the other sound is always a glide, either [j] ("y") or [w].
If the glide comes first, the diphthong is called an onglide (start on a glide), and if the glide comes last, the diphthong is called an offglide (end off with a glide), like this,
Onglide: [ja] ("ya")
Offglide: [aj] ("eye")
As for the word "day", the letters "ay" are pronounced [ej], as on offglide, and it's currently written as [eI].
All the best,