I have a valve core that is oscillating durring a "flowing" condition, I can not have this in my system.

It is obvious that the oscillation comes from the spring characteristics of the valve core.

The question I have is... do all check valves use springs? What other small economical options are there to use a checkvalve design without springs?

Has anyone else ever had this probelm?

Not all, but those that don't use gravity as the restoring force.  Or electromagnetic forces, but that is a solenoid valve, not a check valve.  There are duckbill valves that use flexible, typically polymer, strips that bend apart to open a flow passage, but they are still relying on the spring force generated by bending (they also typically cannot stand very high reverse pressure).

Try changing the cracking pressure rating for the check valve (stiffer spring usually, but sometimes a softer spring quiets the valve also).

General principle:  ANY pressure control valve will sing in the absence of damping.  It has to do with the dynamics of the fluid passing between the control element and the seat.

In your case, you're using what appears to be a commodity valve that really isn't intended for continuous throttling service, hence has no intentional damping mechanism.

You might find an interchangeable core of slightly different construction that has enough accidental damping to make a difference.

If that doesn't work, you may need to roll your own.  How many do you need, and much money have you got?

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