I had a similar problem for a while yesterday with my own "Win a Rosette" objective. Several of the water divines and Greek god divines I checked could not see any available rosettes in any comp type; I presume because all rosettes at that difficulty level already had one divine in them. I did eventually find success with a divine that had high Gallop, as there were plenty of Gallop race rosettes available that didn't already have a divine in them. Maybe see if any of your Greek god divines have high Gallop today and try them?

Do all of the divines you’re trying to find a rosette with have B100?

Because that is a mistake I did many times before; I tried to find rosettes with those who didn’t have 20 wins.

I find that certain types of competitions have none on offer for my divines at times. I think it's because there are so many now and, as only one can enter each competition, they fill up and a new one hasn't opened yet. I wish they'd made all the Ascent divines only able to enter divine competitions as it's hard enough getting rosettes for normal horses now, let alone divines.

Yes I think the constant new Divines from the Ascent are becoming a problem. Its getting harder and harder to get rosettes in all breeds comps because they are jammed with Greek Gods.