Now that the industry has changed a bit, what would you say would be a fair salary to shoot for, for a CJ4? For both a PIC rated co-captain, and a PIC rated captain. Thanks!

Same as before. You’re still a professional.
Get paid like one.

Accepting sub standard wages cause of the corona virus is what starts the race to the bottom.
Cost of living hasn’t dropped, why should your pay?

High supply, low demand, market economics?

So you mean PIC?

what’s this co-captain you speak of?

good question. I guess the difference would be not qualifying time for PIC via insurance

So then you mean PIC rated SIC. That person would get standard SIC pay as there really aren't that many places giving full time pilots 61.55 check outs or bothering with full school for an SIC type rating. The PIC rating really doesn't come in to play for salary.

Co-Captain is just that. It means two Captains on board. Now one of the two may be a "Lead Captain" or "Senior Captain" or "CAM" depending on what company you are working for, but both will get PIC pay.

Side note, for what it’s worth. I know a chief pilot for a 91 operation (private owner). He said his insurance will NOT cover him using SICs that haven’t been to a formal course starting in August. So, no more doing that informal training/FSDO thing.

insurance wants FSI, CAE, etc training proof.

Would the pilots be ‘managing’ the airplane as well, or mostly just responsible for flying?

The OP has a good question. Small cabin PIC rates languished around $60,000 for a decade then slowly moved up to $85,000-$90,000. Only in the last year or two did they catapult over 6 figures.
Unfortunately that wasn't due to pilot professionalism; it was due to supply and demand.
Get as much money as you can. Now is probably better than the fall. If you think we can 'hold the line' on pay when thousands of pilots are out of work and desperate for cash, you aren't thinking logically.

managing as well