I have no idea how Amy words it, here's a few ideas
Early Bird offer
Happy Hour offer
Lunchtime Special
Morning Special
and so on and on...
For the offer to "catch the eye" make sure it's short and concise: it must read quickly so that it has the intended promotional impact.
I'm sure there's no one million ways of putting it so in the end all these offers sound similar. I'm also sure the ones I quote here are commonly in use though I can't tell who uses them and where...