Why don't the Earth's oceans generate a magnetic field? Many questions have been asked here about why the Earth has a magnetic field, e.g.,

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*What is the source of Earth's magnetic field?


*How does Earth's interior dynamo work?


*How can an electrically neutral planetary core be geodynamo?


*Why does the Earth even have a magnetic field?
At the risk of oversimplifying a bit, the answer is the dynamo theory.  Convection in an electrically conductive, rotating fluid – in this case, the molten metal in the planet's core – creates electric currents that, in turn, generate a magnetic field.
Why doesn't the same thing happen in the oceans?  A large ocean like the Pacific would appear to have all of the general properties required for a dynamo.  It is made of conductive saltwater; it has significant bulk flows (indeed, ocean currents are much faster than convective currents in the core); and it rotates with the planet.  Is the higher resistivity the key difference?  If so, would a saltier ocean be able to generate a magnetic field?
 A: As joseph h said, the oceans do have a contribution to the magnetic field, and the reason that this contribution is small is just that the oceans are very thin compared to the Earth's radius. As a result, any vertical convection currents don't have a chance to pick up enough Coriolis force to drive a self-sustaining dynamo.
There are no other bodies in the solar systems with oceans that act as full dynamos either, although especially for some Jovian moons the sub-surface oceans do have a quite marked magnetic interaction with Jupiter's magnetosphere. This is particularly notable for Europa, which does not have a liquid-core dynamo, whereas Ganymede does also have a dynamo core similar to Earth's.
The closest thing to an ocean-dynamo we have in the solar system are Uranus and Neptune. Both have significant intrisic magnetic fields (and magnetospheres), but the fields are very different from Earth's, Jupiter's or the Sun's – namely, they aren't dipoles to any reasonable approximation. The probable reason is that the active dynamo region is much closer to the “surface” than in case of Earth, and the relevant flowing material would have to be some combination of water, ammonia, and various ions.
Schilling et al. 2007: Time-varying interaction of Europa with the jovian magnetosphere: Constraints on the conductivity of Europa's subsurface ocean
Schubert et al. 1996: The magnetic field and internal structure of Ganymede
Stanley & Bloxham 2006: Numerical dynamo models of Uranus' and Neptune's magnetic fields
A: Maybe it's good to point out how this field comes about. You would expect no field as the currents are both equally positively and negatively charged. On their own they don't produce a magnetic field. This only comes about if tboth currents interact with magnetic field of the Earth. These currents are separated because they move through the magnetic field. When they are separated they can produce their own local magnetic fields not canceled by the opposite current (which would be the case if they were not separated),
So if the Earth itself didn't produce a magnetic field the oceons would be neutral.
A: The earth's oceans do in fact generate a measurable magnetic field$^{[1][2]}$. As you have already pointed out, the motion of charged particles generate magnetic fields, so it makes sense that the earth’s oceans would do the same. In fact, the oceans make a contribution (albeit a small one) to the Earth's overall magnetic field.
The moving salts within the oceans have electrical charge which means you have electrical currents, and since the oceans  move in cycles, the motion of the tides etc., as you pointed out,  the oceans contribute to the total magnetic field of the earth.
In the image below, we see how this magnetic field is distributed about the northern hemisphere with the United States and Canada in the center of the sphere, and how its strength varies at different points. The European Space Agency in 2013 launched three satellites, a system called Swarm, which was designed to study the earth's magnetic field in detail and was also used to map the  magnetic field emanating from the oceans.

As can be seen, the ocean generated magnetic field is on average $(1 \ \text{to} \ 2)\times 10^{-9}$ Tesla at sea level.
This field goes to roughly $10^{-9}$ Tesla at the height of about a few hundred kilometers, or average satellite height. This means that this magnetic field is about $20,000 \times$ smaller than the Earth's  magnetic field ($\approx 40\mu$Tesla) caused by the motion of charged particles in the Earth’s core.
References:

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*Analysis of Ocean Tide-Induced Magnetic Fields AGU Journals, 08 November 2019.


*Ocean Tides and Magnetic Fields A short video by NASA and links therein with other interesting magnetic effects of earth's oceans.
