So, right now we upload production code by means of FTP.
I said it would be better to use continuous deployment using Docker, but they said it was overkill (I work at a small company).

Because manually uploading by means of FTP is so much better right...

It depends on multiple factor, here are some:
1. if the devops runs smoothly for several years, its really hard to migrate to another technology. Not all new tech is applicable to current operations workflow
2. Experience. If a large percent of the team does not know the tech, the company wont take the additional costs for training, and if devops workload is high, learning new things is in the far part of the task
3.1 System Architecture. Ex: a server is dedicated only for one particular app/service, it has little advantage of using containers since all resources is owned by the app
3.2. Network architecture. If ftp port is the only opened, need to justify it to nw team
Maybe ask your team to own the lead to a particular project, and prove/influence them to use docker.
I've been doing R and D to use docker to our devops but still cant justify the advantages to our existing deployment protocol (using sftp)

@fun2code We do use git, but not for deployment.
Our SysOps refuse to give us git access in the server.

When it comes to sharing DevOps ideas and new tools to workflow it's not about the tools themselves, but moreso how you market them to your non technical colleges. You, the pro in this area, know this shit will help but the technical skill to set it up or onboard it scares non technical people.

"It was working fine before you introduced this so this is just extra work." -typical roadblocker by non techncials.

Sell it too your colleagues as this idea will save time or money or both by being able to do "x" or "y" for us and replace that old tool which we couldn't do before.

Setup a small demo or test case to highlight and show the direct business value. Usually this instills the logic for a senior member to then champion this idea higher up, and offer to help in that presentation if needed to answer stupid technical questions about it should it arrise.

All else failing, see if any of your direct competition is adopting "x" and use that case to your advantage by saying "the company's evolution is slowing down and "x" gets us back to that competitive edge because info and insights that competition get that we don't is a disadvantage for us, and we don't want to be disadvantaged, right?"

It's all how you sell it to them. This has become its own little art form for me trying to onboard and improve our DevOps workflow being lowest on the totum.

@Vip3rDev sounds good.
The DevOps agree with it (since I am the DevOps xD), however, the SysOps don't want any of it as it "is more work for them to setup"...

Developers aren't the issue (they want to learn how to do it), the DevOps aren't the issuex since that's me.
Only the SysOps are the problem (with everything in the company tho... they are a bunch of slackers (which is why I switches from SysOp to DevOp)

Oh my god instead of something fancy and complex go with just git.

@py2js but then how do we deploy? :p
Cus SysOps aren't gonna do it I don't have a VM or something to do it on, and the management just doesn't care xD