Try this: hum the melody of the song.
Pick out the notes in that melody on
one or two strings. Then practice to
become fluent at playing the note
sequence.
When the melody is secure in your fingers,
try adding a second note in unison with
each of the melodic notes- its a bit hit/miss,
but you'll notice some notes sound good in
tandem, and others don't.
Once you've done that, try adding a third
note to create a triad.
Also try different positions on the same chords-
for example, if you move a B-flat shape up
to the fifth fret, it gives you a very nice variation
on a "D" chord, without having to barre anything.
When you are playing the chords of your songs in
sequence, try this: Pluck each of the stings of the
chord, and see which one is the root (melody) and
which ones are the harmonics.
When you practice, really take your chords apart
and listen to them!