In just the 20th century....

USA vs Mexico 1914 -- both democratic republics
USA vs Haiti 1915-1934 -- both democratic republics
USA vs Dominican Republic 1916-1924 ...
Democratic Republic of Georgia vs Democratic Republic of Armenia 1918
Armenian Democratic Republic vs Azerbaijani Democratic Republic 1918-1920
Ecuador vs Peru 1941 - Present (most recent big flair up 1995)
India vs Pakistan 1947 - 1948, 1965, 1984-87, 1999
El Salvador vs Honduras 1969
Rwanda vs France 1990-93