The Amazon Fire, 7" tablet, is going to be 35 dollars on Thanksgiving.
It only has a 90 day warranty, so that might be an issue if your younger child might throw it or something. They have a more expensive ($100) 'kid's' edition that I think is the same hardware, but with more kid friendly software and it has a 2 year no questions asked warranty and a built in rubber bumper case. I'd make sure that counting app is on Amazon's app store if you consider going this route.
Another option might be getting a cheap pre-paid phone and not activating it. Using it as a micro-'tablet'. The main risk with this is that all phones, even without sim cards, are capable of making 911 calls. You can remove the dialer from the screen, but there is still going to be that risk.
For the other tablet, I don't have a solid recommendation, but a couple of thoughts. One idea that comes to mind is the Lenovo Yoga Tab. They have an 8 inch model that has a very unusual design but it has a crazy long battery life and supposedly better speakers than a typical tablet, though it might be on the heavy side for a child, I really can't say. That same guy I linked in the first paragraph wrote about it a while back, about a way to get a coupon from Lenovo for it. I wouldn't be surprised if they have a slight price cut for black friday, but that is a guess. You might also look at the Galaxy Tab 4, but the hardware is 18 months old at this point and Samsung isn't the greatest at keeping Android up to date, but I have a just-turned-4 year old Galaxy Tab and it has just been the past few months when updated apps are not running well and some apps no longer work. That would put the Galaxy Tab 4 at about the halfway point of it's maximum usefulness, if it follows a similar trajectory, I mean.
That is so weird the youtube app quite working on the iPad. There must be so many iPads out there that are living out their years as couch tablets and second screens that need that sort of function. Check out the comment/reply with the green checkmark on this thread, it might be worth a shot trying it.