This guide is not written by me. The original author of this guide is kenneth and the information below is retrieved from his blog: http://dotnettrend.blogspot.com/2012/09/how-to-recover-mysql-website.html
I faced this problem too, before reinstalling MySQL Dot Net Connector, I tried this and the icon get back. Therefore I repost the guide and share it here.
Written by Kenneth....
Visual Studio 2010 has been updated to SP1 but a weird symptom happened while I came back and revisited my favourite icon of MySQL Website Configuration Tool over the Solution Explorer. It was just missing!
After a series of upgrade and re-installation of MySQL .NET Connector package via URL:
The icon is still missing and someone might think it would reappear on creating New Web Site template. However, that's not the case for me.
Before I reinstalled the whole thing for VS2010, I got my last hope to see if any miracle could happen.
The fix I have done is just as follows
Click on the the solution in the Solution Explorer.
In the Properties Window, click "Property Pages" icon.
A project properties template is shown up in the content window.
Try a couple of clicks on the items and then save it and close it.
See if that MySQL Website Configuration Tool icon reappear again under Solution Explorer toolbar?