Chest InfoPlease note: These rewards are only from a fully boosted marriage tree. If the tree is not boosted full (with for example insignia) it gives less rewards (for example only 5 runestones instead of 10) and less chests. Fully boosted tree gives 5 chests twice per day.
Items from the Marriage ChestsThe most common items by far are the 1-3 Gem Pack and the 10 Runestones with 28.9% and 28.2% chance of dropping respectively, so 1 in every 3 chests roughly speaking. That's actually pretty cool since gems we always need and runestones, even if we can get lots of them, are never enough to max out our runes (especially with advanced runes).
Another very useful drop is the 11.6% chance of getting Fashion Core Shards, which means that in about every 100 chests you can make a Fashion Core!
From there on the chances drop a lot down to about 1% of getting things like the Eternal Heart, 100% Experience Scroll, Crypt Key and the 99 Roses. The 99 roses seem to be more frequent though, at 1.0% in the data versus 0.6%-0.7% of the other two.