Yes, you could make one but at $30 I'd recommend purchasing one if your goal is just to have the modulator. If learning is what you want then by all means - do it. Lots of good circuits out there. FM transmitter would be a place to begin. Just be aware that simple is just that - and the simpler ones aren't stable, sound isn't good, etc. I do know folks who have purchased units such as you describe and they are happy with them. Not perfect but very good sound. They run the MP3 player music thru to FM radio in rental cars.
As a different twist you might look to Ramsey or other kit suppliers. Some have high quality, stable transmitters - for not a lot more than $30. You can learn a lot, there is less struggle, etc. Just a thought. As far as I know, most or all are compliant with regulations - low power, etc.