I don't know why but I always feel strange when I read dc x dp and it gets mentioned that "Ghosts are real?", Deadman exists. The JL literally knows ghosts and other supernatural being exist. I get the speedsters being deniers, but the batfamily? Nah, they definitely know. So I give you:
Dick adopting ghost Danny (de-aged version bc he's cute)
Dick kept the obol coin on him just in case, and even with it it had maybe taken a bit for him to accept that the toddler, the tiny four year old white haired child, was dead.
Danny, as he had introduced himself - while talking to the ghost of the man whose corpse Dick saw both standing in.
Danny likes Dick's puns, so after meeting a few times he went with him to Dick's place and eventually stayed there.
Dick kept getting hit with worries, kindergarten? Can't register a dead child. Clothes? Dead children apparently don't need to change. Bath time? Danny refused help "I'm already dead, not like I can drown!"
Danny gets brought to the manor exactly once, gives Dick the nasties glare and silently lets Dick's siblings coo over him before hiding in Damian's barn until they were leaving. Bruce missed the chance to meet Danny because he had a JL meeting, he still tries to get a date set when he's coming to Blüdhaven to meet the little guy.
Danny stays a toddler for a few years, until one day Dick is just getting surprised by teen Danny playing games in the middle of the night.
Dick really thought people joked when they said that children grew up faster than you noticed...