We mapped the available glyphs and accents for the Amis language.
The letters in alphabetical order:
    a c d f ng h i k l m n o p r s t u w y
Everyone of them can get an acute or circumflex accent on top. ng can get a dot on top of the g.
The accents are literally on top: i would get the dot PLUS the accent on top.
Not all accented characters directly exist in Unicode; however Unicode developed various kinds of combination features to take care of these cases.
Then we need an input method that would insert ng instead of g and allow to type all the accent combinations.
Here is the full character set:
    a     á    â
    c     ć    ĉ
    d     d́    d̂
    f     f́    f̂
    ng    nǵ   nĝ  nġ
    h     h́    ĥ
    i     i̇́    i̇̂
    k     ḱ    k̂
    l     ĺ    l̂
    m     ḿ    m̂
    n     ń    n̂
    o     ó    ô
    p     ṕ    p̂
    r     ŕ    r̂
    s     ś    ŝ
    t     t́    t̂
    u     ú    û
    w     ẃ    ŵ
    y     ý    ŷ
Update: this character list has been improved and the good version is found in the Debian wiki.
The list is not displayed correctly with many fonts or rendering engines. Arne made a test page that explicitly sets a font that works.
The accents are not taken into account when sorting.
Uppercase letters are not used.
Note: the page has been updated to reflect further input from Unicode and Amis people.
Update: there is now a wiki page on the Debian wiki.