I have the same Moore/Muir family with a link to the name Foster.
My GGrandfather married a Maria Moore/Muir around 1858-60 in Monaghan accoring to the birth cerificate of their son. The Parish was pretty elegible on the certificate but began with Drum... it looks like the Monaghan Parish of Drumsnat is the most likely match. Maria and her husband moved to Scotland very soon after the marriage. The family story was that it was a Catholic/Protestant marriage and the couple eloped (or escaped?). Their second son my grandfather was given the name Foster (a very un-catholic name at that time), and as yet I haven't found the source of the name. Maria's parets were William Muir and Sarah Brown. You will note that the Family name is alternately recorded Moore or Muir.
During my search for a 'Foster' I did find a Foster Muir in Coatbridge, Scotland who also hailed from Monaghan of similar ages with Maria, and who by coincidence? recorded his parents as Archibald Muir & Sarah Brown... Brother, Step Brother, Cousin..., or simply coincidence. They all lived and died in Coatbridge, and at times living very close to one another, but as yet I have definite links