The thing with parodies is you really need to follow the same scansion and rhyming pattern of the original. Most of those in this thread try to squeeze alternative words in standard four four rhythm into the distinctive Greensleeves three four timing. Similarly, the rhymes in the verses should not be straight single syllable rhymes (usually referred to as male), but rather extended three syllable rhymes, and at the very least alternating rather than closely paired, like this:

Alas, my love, but you…… do me wrong,
To cast me off so dis…….courteously;
No English rogue, but I’m…….truly Scots,
That’s why I wear this old…….skirt, you see.

OK, the third line doesn’t cleanly rhyme (with line one), but it’s the first of the three syllables that most need to rhyme. I don’t why people say I’m pedantic…