Lucas Oil makes some small applicator bottles that seem to be pretty leakproof.
https://lucasoil.com/products/out-do...oil-applicator
There are other similar bottles out there, but the rubber/plastic stoppers don't always fit tightly. These seem to be a very tight fit. Mine haven't leaked so far, but I don't lay them down on their side or upside down and I haven't thrown them around either so I guess I haven't really torture tested them.
I've had decent luck with these Brownells needle oiler bottles but they don't seem as heavy duty and I'm less confident in their ability to remain leakproof over time or under heavy use. The rubber/plastic stoppers come off pretty easily and I don't use the bottles for anything other than a bench situation where they're going to remain upright and won't get bumped around.
https://www.brownells.com/gunsmith-t...prod44434.aspx