This is a Gaelic phrase, which means "my right forever".
Here's how to pronounce it:
* mo - (moh) like the English word "moan" but shorter
* chòir - (chore) the "ch" sound is like the "ch" in "loch" or the German "ich"
* daonnan - (don-nan) the "n" sound is similar to the "n" in "sin"
Putting it all together, the pronunciation is:
moh chore don-nan
Note that Gaelic pronunciation can be tricky, and this is just a guide. It's best to listen to a native speaker to get the full pronunciation nuances. You can find recordings of Gaelic phrases online.