I think this is great idea, but you've got to start small. Remember that for a two year old, their attention span is one minute per year. So, be clear about where he is supposed to be. You might consider using a tension/baby gate in his door if he needs a physical boundary to remind him that it's 'quiet time'.
I always suggest starting with a shorter amount of time the first few times. He needs to have faith (through experience, mind you) that the timer WILL ding eventually and that you will come and get him. When my son was about 3 or so, he was up to about a half-hour on his own-- it does take time. Our kids look upon us as the BEST playthings in the world, and you are asking him to not be entertained and to use his imagination and keep himself active. This is a huge task for a two year old.
You might ask him to have 'quiet play' time in his room for a short time and then tell him that he might sit on the bed with you and look at books quietly-- but only if he's being quiet. This isn't a storytime. Another angle is to say "Mommy needs a quiet time" and go into your own room. Make it about YOU taking YOUR time, and ensure that if he's unsupervised, he's limited to a very safe place. (again, a room with a gate is perfect).
I don't know ANYONE who has their kids take a 1 hour quiet time alone in their room at two. Nobody. And this is from 20 years of working with kids. That's a Holy Grail sort of thing-- a unicorn- a completely mythical idea. It's not about the amount of times you keep reinforcing it, either.
You could use the TV show as the 'reward' for quiet time. "You may play in your room until the timer goes ding, and then you may have a show after the timer goes ding." Just use a plain kitchen timer (it doesn't need to be kid-friendly, he's two, he's not going to understand it anyway, just play with it) and put it up high where he can't reach it.
For longer stretches of time, I have found that setting up a sensory play activity in the kitchen helps immensely. I used a big old quilt on the floor and a washtub (any decent sized bin will do) and gave the kids scoops and rice, or beans and funnels, tubes (toilet paper and paper towel tubes are great), sometimes it was rice and a few trucks, a couple shovels, etc. If you Google "Sensory Play" you will find a wealth of ideas that cost hardly anything at all. I actually invested in a big zinc washtub and we still pull it out-- my son is 6. Sensory play is a lifesaver, and with a quilt, the mess can be folded up into the quilt, then dumped in, it keeps the wet or messy floor safer too, so they don't slide on the materials they are using.
Good luck and I really appreciate you not using media time-- I find it tends to make kids MORE cranky when we have to turn it off, and it doesn't always allow kids brains times to rest-- the brain is constantly chemically responding to new images and gets a nice shot of dopamine while they are watching-- but the withdrawl of that chemical can make the after-movie transitions a bummer. Play can be restful, a lot of research shows that open-ended play is actually very therapeutic and educational for kids-- all without our doing much as adults. This is what we consider 'down time' for kids and I have seen that the more time kids have for open-ended play, the happier they often are. (And I know some kids do give up their naps at this age, so it just depends on the child.)