element fusion, which makes a create collection of online webbuilding, formbuilding and emailbuiling services, called water, light, and breeze faced something similar. (breeze.com was taken, etc)
so they paired each with a verb (embracewater, feelbreeze, etc).
37signals did a little appending for their products as well (backpack is backpackit.com, basecamp is basecamphq.com)
using your SingIt.com example, singitoutloud, singitloud, singittogether (social network implication) and brand the heck out of it.
People will hear your company name ("sing it") and try to go to the dot com version, that`s just conditioning/expectations. But with a real effort on branding, you can hook your name with an extra meme that`ll help folks remember you.