In Polish we have 9 such characters and most people use just so called "programmers keyboard layout" which uses left-alt + letter to do the accent.
E.g. alt + e = ę, alt + l = ł (with a one case where we have two different accents for a single letter: z, so we use alt+z = ż and alt+x = ź, the second letter is less commonly used then the first one)
20-30 years ago there were some strange keyboard layouts that didn't use alt, but hopefully they were forgotten.
Some people move to BÉPO or something like that, I use QWERTY with Xcompose.