How would you influence your co-worker who might be undecided about getting the COVID-19 vaccine?

I've stopped bothering to try. I'm vaccinated, so I will be fine, and everyone in my workplace who wanted to get vaccinated did.  As far as I'm concerned, if the holdouts get sick, too bad, so sad.  I have zero sympathy for anyone who chooses not to get it if they have no health-rated reason for not doing so. 

I think a lot of people don't understand that while some people may just have flu-like symptoms for a few days, many others have 3-6 months or more of debilitating symptoms, and may suffer from after effects later all their lives. I had a conversation with one person who said that the vaccine had been developed too quickly. I discussed how scientists had been working on this vaccine strategy against other COVID diseases like SARS for years- from before this person was born. I can't be sure that this had an effect on her, but she and my other students know that I have been vaccinated and have not suffered from any after effects. 

I wouldn't attempt to influence my co-workers. 

If they asked, I'd be honest with them and tell them the pros and cons.  Most of which i doubt you know.

-- For starters, Pfizer and Moderna vaccines are not "vaccines" they are immunology therapy.  J&J and AZ are a traditional vaccines

-- "safe" if they are "safe" why did the US government give vaccine developers and manufacturers immunity against lawsuits?

There are pros too but that would depend on the specific situation.