"Yuyyu~n <3Reimu can even sing a song!Yu~ Yu~ Yukkuri~"
Not translating yukkuri is a good choice for this picture, I think.
Eh, it depends on how you pronounce it, like with many sound effects. Instead of pronouncing it in an "American" way, yukkuri, it sounds more like singing if you pronounce it the Japanese way "yookiri!"
Also, the "~" indicates that you stretch and fade out the vowel, right? So in this case it would be "Yuyyuuuuun" right?
What I meant by not translating is that "Yu~ Yu~ Yukkuri~" makes more sense than using "Yu~ Yu~ Easy~" or "Ease~ Ease~ Easy~".
Honestly, I'm still not quite sure just what the ~ means. When I RP, I just think it means that there is a lilt to the voice, or that it's singing (much like the use of a music note). I should go ask some Japanese people tomorrow.