Too many issue for a youtube to mp3 converter website. Luckily there are a lot of ways to do a simple youtube to mp3 converter page by using public api / widget of some services.
Here is the top Youtube to MP3 API sorting by easiest to use:
YoutubeMp3Free.org is most trusted service that allow user to convert youtube to mp3 for free. And their API / Widget is not only easy to use but also powerful and customizable.
YoutubeMp3Free.org Widget Generator:
YoutubeMp3Free.org Button Generator:
You must input url to generate button, it's a one-click button, when user click, it will download directly mp3 to user's drive instantly.
YoutubeInMp3.com provide another solution for user to use their api, they have widget generator, api to get result.
Convert2Mp3.cc is a simple solution to integrate youtube to mp3 function to website. You just need to include the script, and modify the anchor link. The only thing i don't like is they redirect to their main website, not direct download button.
About is the top list Youtube to MP3 APi / Widget, you may want to add another one, please let me know by leaving a comment to this post.