She had given birth to her and the fellow pop star's first child, son Bear, in March.
"Happy 1st Father's Day Liam.." Cole wrote, alongside a black and white photo of Payne. "You are the most amazing daddy and the best example for our son. The way he looks at you says it all. Your relationship melts my heart. You are the centre of his world & We adore you."
Cole and Payne had announced the birth of their child days after he was born and a day before the U.K.'s Mother's Day 2017, during which he wrote, "I'm completely in awe of his incredible mother and how she has been the whole way through this, she's really made my dreams come true."
Earlier this month, Payne gushed about Bear and Cole at a live-streamed Q&A event with fans to promote his debut solo music video, "Strip That Down."
"I'd say bath time is the most amazing thing, is the funniest thing," he said. "He's great, little Bear, he's just learning now to giggle, these past couple of days. We got the first giggle out of him the other day. I've slowly noticed that as l come over and I'll pick him from where ever and [get] a lovely little smile out of him, He smiles just like his mum and his mum smiles beautiful."