I spend so much effort trying to distract my kid from just asking to watch TV, then as soon as I get some time to myself it's straight onto the TV or video games (or phone). Maybe I need to practice on myself as well?
How old is the kid? They might be ready for you to read chapter books to them at bedtime. I remember being about 10 and getting lotr and Brian jacques read to me.
For 'can I watch something' - predictability is key. If they have a chance of trying to wear you down, they'll take it. Settle for something like: you get 1 little bear after daycare, and that's it for the rest of the day.
As other guy said tho, that means you can't watch either tho.
The other thing I've learned is not to cater media to kids. E.g., every time I get in car we don't listen to her music. I'll put on the radio and sometimes she tells me 'I like that'. Who knew kids would like Foo Fighters Everlong because it's relaxing.
Or that my 3 yo will watch Jane Austen movies with my wife?
Hmm... We're trying to make sure we all get turns, so she gets nursery rhymes to sing along and do the actions to, then we get some pop, rock, folk or metal.