The other way is in the safari zone. Go to a patch of water and fish with the super rod and keep fishing until you get one. You can do this as many times as you want because you are not taking any steps so keep fishing. When you encounter one follow these steps.
- Throw some bait.
- Throw a rock.
- Throw a ball.
- Hope for the best!
- If you fail, try again.
The other way to get it is by going to the game corner and getting it with coins.
- Go to the Elite Four or other trainers that give you a lot of prize money.
- Save up a lot of money and take it to the game corner.
- Go to the counter and exchange it for coins.
- Buy Dratini.
Sources: http://strategywiki.org/wiki/Pokémon_Red_and_Blue/Safari_Zone and Experience.