The oldest child a daycare will accept still in diapers and not potty trained is usually 3 to 4 years old, although it also depends on the specific daycare and the daycare's own policies.
Many reputable daycare centers will still accept kids in diapers up until around 3 and 1/2 to 4 years old, but usually the child needs to be working on potty training by 3 to 3 and 1/2.
I've worked at a few daycare centers that would not accept any kids that were not potty trained by 3 if they were new.
However they would continue to care for the 3 year old and above until they were potty trained if they were already in their care.
Most reputable daycare centers will also assist with potty training your child.
However the keyword here is "assist" which means that while daycare centers will usually assist and help with the potty training, it must be the parents who first start the potty training initially at home.
Parents must also continue with the child's potty training at home even when the daycare center is assisting with the potty training.
Most daycare centers will also require that your child wears pull ups for at least 2 weeks or so and be able to keep those pull ups dry for those 2 weeks before they can come in underwear.
If your child is continuing to have accidents and not really working on the potty training or is actively resisting potty training at daycare then the daycare may require the child to wear diapers until they can be fully potty trained.
But it can vary depending on the daycare center.