family search ireland births and baptisms 1620/1881 shows the following children for this couple some no first name.
7 march 1873 palmer.
27 may 1874 ederney fermanagh,palmer
9 june 1876 fermanagh. johnston christopher palmer.this child could possibly have died and the next one as per the date you gave being called same name.
30 march 1878 fermanagh, palmer.
24 nov 1879 drumard fermanagh ,palmer.