I did some digging on the web and found references to 'Yonah Matzah' but couldn't find any lyrics sheets or recordings. Fortunately, the folks on the Shamash.org Jewish Music mailing list came to the rescue. The title is 'Yom Shabbaton", "yonah matzah" is just part of the chorus. We even had the lyrics in a USY bencher. (A bencher is a handy reference book or pamphlet with Shabbat and holiday blessings, zemirot and the Birkat Hamazon (Grace after Meals))
It turns out that Yom Shabbaton is a very popular zemer. There are a lot of recordings available online, including at the USY Z'mirot project, and SiddurAudio.com as well as a number of CD's. The CD tracks I've listened to don't move me much, but the SiddurAudio is spot on. A bunch of folks with good enough voices and a lot of heart singing the kind of lovely melody I want to hear at my family table every Shabbat.
I don't have a good primary reference, but a number of websites attribute Yom Shabbaton to Judah Halevi the 10th century Spanish poet and philosopher. I also don't have a good translation (yet) for Yom Shabbaton but the website for the Vocolot/Linda Hirschhorn recording "Gather Round: Songs of Celebration and Renewal" provides this:
Yom shabbaton eyn lishkoach.Exactly.
Zichro kereyach hanichoach.
Yonah matz'ah vo manoach
vesham yanuchu yegi'ey koach.
[A day of Sabbath rest.
As hard to forget as sweet scent.
The dove finds comfort
and there the weary rest.]
More information about zemirot can be found at the JewishEncylopedia site.