The "Catastrophe" star lost his son Henry in January, following the toddler's battle with cancer.
In a tweet on Monday Delaney wrote, "Today would've been our beautiful Henry's 3rd birthday." He shared links for two charities that center on hospice care for children if followers wished to contribute in honor of the day.
Delaney also tweeted photos of Henry as a newborn and shortly before he died.
"Here's Henry not long before he died," the actor wrote. "You can see his little tracheostomy tube on his neck and his left eye is turned in due to nerve damage from surgery."
"He has a bus & a turtle though so he's happy," Delaney added. "He was such a sweet boy."
He revealed his son's passing in January via a social media post.
Delaney said Henry was diagnosed with a brain tumor in 2016, shortly after his first birthday.
The youngster underwent surgery and treatment through the early part of 2017, but the cancer returned.
"Henry was a joy. He was smart, funny, and mischievous and we had so many wonderful adventures together, particularly after he'd moved home following fifteen months living in hospitals," Delaney wrote when he announced his death.
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