Thyme & Time

Now I just need homophones for parsley, sage, and rosemary. And Garfunkel.

Flea & Flee

-ea – parasitic insect.
-ee – run away!
As in, "Run away from the parasitic insect!"

Tear & Tier

I always cry at weddings... from boredom.

Marten & Martin

With an E – small carnivorous mammal, a member of the weasel family.
With an I – small insectivorous bird, a member of the swallow family.