Baby's Tears (soleirolia soleirolii)
Ron

Dicentra Golden Tears
Passiflora 'Crimson Tears'
Achimenes - common name "Mother's Tears"

Not flower names but interesting:

The flower symbolism associated with the lily of the valley is "Our Lady's Tears."
Like the lily of the valley, the flower symbolism associated with lungwort is also "Mary's Tears."

I found three: Commelina coelestis, trandescantia virginiana, and tinantia erecta that have the common name Widow's Tears.

Thanks everyone! These are great ideas!

I found some others while searching online:

Daylilies - Russian Tear, Golden Tear, Golden Tear Drops

There were two others, but I'm against them after reading how invasive they are and that they are considered weeds.

This is a great start though!

Ollierose, I can't help but ask, since I am part cat and curiosity surely will kill me someday: why the garden of tears? Is it a memorial garden? I would love to see pics when you get it all planted out.

On a lighter alternative, my kids have some friends that are described as "emo" (aren't ALL teenagers emotional wrecks!?!), and this might be a healthy way for the kids to have an emotional outlet--to plant a crying garden could be better than Zoloft or any $350/hour therapist, regardless of the cause of emotional distress; not to mention, there might be a new lifelong gardener in the making. Gardening truly is theraputic for me!