It just occured to me that I wanted to start working on this new project which aims to swap the animobject of the animation where your children are playing with their doll, to cover mod-added toys that you've gifted to them. So instead of the vanilla doll AO, your child may instead appear to play with a different toy, as long as they have it in their inventory.

If you want to test the animation, open up the console, click on the actor and enter "sae idlechildplaydoll".
Before you ask, yes, even works on the player character, given that you're carrying the item.

Note: If a child is carrying multiple toys, they may only favor one of them instead of picking one randomly for each playtime. Right now I have no clue how to randomize that, so help would be appreciated.
But I can recommend that you install the RDO Update, turn your child into a follower, ask to trade with them and then take the toy that you don't want them to play with anymore.

WARNING - Depending on the toy, there odds are high that there will be some clipping during the animation.

So far I've covered toys from the following mods:
Additional Hearthfire Dolls
Burger Jarl
Serana Doll
Skyrim Toy Story
Decorative Doll Update (Patched for the regular version and ESL version respectively)
Toymania (This one requires the main plugin)
Craftable Gifts for Children (just missing the basket)
Teddybears
Rockinghorses
Children Toys - Deepening Elements of Skyrim
Bloodchill Manor CC
Blahaj - Plushie Shark
*NEW* Skyrim's got Balls (sorry for the extremely long wait)

Suggestions for more mod-added children's toys are welcome.

The main plugin makes sure that boys can also play the doll-playing idle, and that the idle will work with any item that has the "BYOHAdoptionToyKeyword".
From v1.5.0 onwards, the main plugin now also expands the animation pool for the doll-playing AI package and idle marker, so children can now read books or play instruments if they have the necessary items for that. Should work well with Expanded Children Gifts.

I also highly recommend that you check out GroundAura's Formlist Manipulator patches, especially if you're running multiple mods that adds more giftable toys.



Requirements:
AnimObject Swapper

Installation:
Either download with a mod manager of your choice, or manually download the archive and extract the contained Data folder into your Skyrim SE folder.
(C:\Program Files (x86)\Steam\steamapps\common\Skyrim Special Edition)
Then enable the plugin in your plugin manager, such as Wrye Bash, or the Skyrim SE launcher.