www.Lush.com sells deodorants called Krysztal...they work great but can cause irritation if applied directly, or if the armpits are not completely dry dfrom bathing first....
I find using a brush to brush it on works great.
These come in several varieties, one has tea tree oil called T'eo. I use Oxeo Cube--smells great, works fine.
Very inexpensive and long lasting and biodegradable and no plastic packaging!