I love the fact that he is willing to earn it. New or used is not really the question, he came in with a question about ideas on how he can earn money. He is willing to work for whatever bike he gets.
At 14, most of the ideas for earning cash are listed here. I think the most lucrative ones are Mowing Lawns, Washing Cars, and Baby sitting. Paper routes are nice, but the amount of time it takes to complete the rounds and the collections is way too long for the money you earn.
You need to look at the ratio between earning money and the time taken to earn that money. That breaks down to $ per hour. Use your time wisely, don't waste it on lower paying jobs if you can earn money faster with other odd jobs. I don't know what the going rate for paper routes are but as I recall, they were never the fastest way to make money, but it was stable work. However, if it takes you 10 hours of folding, delivery and collection to earn $50 but in 10 hours of detailing a cars you can earn $100, obviously spend that time detailing cars.
By the way, a good detail job costs over $100 easily and can be done in 4 hours with practice. I know people that pay professional detailers $300 for a complete detail job. However, even washing/waxing a car can earn you a fast $30 in some areas and can be done in about 1.5 hours depending on the size of the vehicle.
Mowing lawns is another quick way to make some cash. Most kids in my neighborhood charge $10 per lawn to mow/edge the lawn and it takes them about 30 mins per lawn to complete. $20 an hour aint bad money and these are typical residential lawns, not big acreage.
Babysitting can be pretty good as well. My daughter charges about $5/hr per child. If she has a family of 3 kids to watch, that is an easy $15 per hour. Obviously, the key here is to land families with multiple kids. Evening sitting jobs can be great because if the kids are young, they often go to bed early leaving you time to work on school work, etc.
Don't forget, you still have school work and responsibilties around the home to take care of. Don't sacrafice school work to raise money to buy a bike. Education is the key to your entire future. With a good education, you can land great jobs that will afford you many nice things including bikes.
In the end, you have a great attitude, keep it up and you will have a bike before you know it and be out enjoying the fruits of your labor!
Go get em!