Use the diatonic harmony trick of stacking notes and see what you come up with.
For instance, in G, the notes of the major scale are
G A B C D E F#
If we stack every other note in that list (wrap to the beginning when necessary) 3 times we get a simple minor or major chord/triad:
G,B,D - G Major
A,C,E - A Minor
B,D,F# - B Minor
C,E,G - C Major
D,F#,A - D Major
E,G,B - E Minor
F#,A,C - F# Diminished
If we stack 4 times we get a more flavorful chord:
G,B,D,F# - G Major 7th
A,C,E,G - A Minor 7th
B,D,F#,A - B Minor 7th
C,E,G,B - C Major 7th
D,F#,A,C - D Major 7th
E,G,B,D - E Minor 7th
F#,A,C,E - F# Diminished 7th
You can keep stacking but at a certain point things become pointless. 5 stacks usually ends up in some kind of add 9 chord with the third and seventh chords in the list becoming a flat 9 (9th lowered one half step).
If you have a song in a minor key, use the corresponding minor scale to do the stacking.
You can take the above and do chord substitutions as well, such as the 5th of the 5th sub and the tritone substitution.
Here's a more complete explanation of diatonic harmony based on the major scale and here's one based on the minor scale.