I am guessing that he's not able to go to daycare because he's not fully potty trained. Would having him have a BM before he goes to daycare (so no accidents there) mean he could go? Not sure I follow.
Adults can be somewhat regular in the mornings because when we eat, it stimulates our colons to rid ... etc. for some people. The main thing though with adults is caffeine - a colon stimulator. That's why it appears that for some adults, they are really regular.
And there are some adults who are on very rigid diets - eat the same thing every day, at the same time (think older people), have the bran ..and who are just regular. I do think some feel they can train their bodies to go at certain times. Maybe you can ...
However, to do this to a child who is potty training - I don't think is a good idea. I've never heard of this with BM's. Nor pee to be honest. You go when you go. The reason you can say Go have a pee, before you leave the house is because generally there's always something there. It's not the same with a BM (not with my kids anyhow). I've never been able to say that. Ever.
So I wouldn't waste my time if I were you. That would be my advice. Also I think it might screw up your potty training efforts. I let my kids sit with a book sometimes on the potty (that was in initial stages of training but more for pee) and that was for fun only, just initially.
*Utimately - the more you frig with their natural body processes, the more messed up it will be later on. I had a friend who really did a number on her kid with potty training. It got so that her kid would only have BM's at her house with a ritual - so if he hadn't gone in the morning, she couldn't go out of the house in afternoons. Then she had to have another ritual to break him of that ritual. A lot of stress really.
Good luck :) It will come. I always kept a potty nearby my kids (even while playing) and just hung out with them for a weekend, with them in underwear only and looked for cues. When I saw they looked like they were 'straining' then I said "Oh here we go!" and they clued in that straining meant a BM was on the way and to sit on the potty. Very soon after, they could walk to the toilet and have it there.