Every action has an equal and opposite reaction
Assuming access to massive amounts of energy - the gravity shield might be very effective but how good are those station-keeping thrusters?
The force applied by a gravity generator still needs to be dissipated somehow. A ship accelerating a projectile will experience recoil via the gravity generator. A ship with a gravity shield stopping an inbound projectile of 1 kg travelling at 1m/s will receive 1 joule of kinetic energy from the projectile.
In order to stop a projectile of 1kg travelling at 0.5c the ship will need to dissipate 10^17 joules of kinetic energy. Deflecting a projectile at an oblique angle will transfer less energy but will impart more rotation. Deflecting multiple dozens of incoming projectiles may make the ship uncontrollable. If the ship has no ability to station-keep then it will be lost - how much rotation can the hull withstand with no way to dissipate the energy? Just one 1kg projectile at 0.5c could cause the ship to spin itself apart.
Another implication of this is that the gravity generator itself needs to be mounted in such a way that it can withstand the forces it will need to impart to various objects, but this could be hand-waved away with magical meta-materials.
Here's how I imagine station-keeping could work in this universe:
A ship could use the gravity generator to stabilise the ship against a nearby object if one is available, but this might mean that a ship can only effectively maintain it's position under fire whilst within range of a massive object such as a planet.
If a planet isn't available then the ship could stabilise itself against something which I will call a "kinetic gravity node" - a special kind of ship whose only job is to transmit kinetic energy, via it's gravity generator, to another node - and another, and another - until it reaches an "anchor node" which would be a node within range of a massive object.
This would mean that for effective station-keeping in battle a chain of nodes would be required and these nodes would be a critical weakness in any fleet's ability to fight. An enemy would seek to disable the node chain and disabling it would grant a massive advantage.
Or hey maybe you just cart a supermassive black hole around with you wherever you go. Just slip it in the glovebox.
In addition to the nodes, ships could use gravity thrusters as a backup and carry a quantity of reaction mass which will allow them to station keep by expelling a stream of matter at ridiculously high speeds. In this case there is still the issue of how much they can carry and what happens when it runs out - however much fuel they could carry it will still have less available kinetic dissipation potential than the nodes, which have theoretically infinite dissipation potential.
Shield defeating weapons
I thought about whether or not a black hole fired directly at the shield would be able to penetrate it and I think the answer is probably not - from the shield's perspective it is just deflecting mass and as long as it can provide the energy necessary to deflect the mass then it doesn't matter what form the mass takes.
Gravity grapples / ship catapults
If you can't penetrate the grav shield then how about trying to accelerate the enemy ship into a nearby sun? This would only work if you can overcome the enemy station-keeping mechanism, which brings about a ridiculous concept: the gravity node tug-of-war.
If you were able to lock onto an enemy ship and apply force via a gravity generator then the force could be transmitted all the way back to the anchor node. If the enemy node chain terminated at a planet and your node chain terminated at a much more massive object like a sun then you could move the enemy anchor object. Now the ship itself might not move because it's still transmitting the energy back through the chain and the anchor object is experiencing all of the effect, but half way across the sector the anchor planet might already be headed into a nearby gas giant. Unless you know what the enemy anchor object is you're effectively working blind - you have no way of knowing that your grapple is having any effect at all - you would only find out if the enemy grav chain stops working, and the targeted ship could just switch to thrusters and try to outmanoeuvre you anyway.
Nonetheless it tickles me a bit thinking about throwing a random unseen planet around.
Critical mass / singularity detonation
There is a universal limit to the amount of energy which can be in one place at one time, beyond this limit you will get a black hole. This isn't the same as throwing a black hole at the enemy ship, what you would need to do is cause the enemy gravity generator, or one of their gravity generators, to exceed the energy limit for a schwarzschild radius matching the size of the gravity generator. If this happens then it doesn't matter how much energy is available to power the generator, it will immediately collapse into a subcritical black hole which will then immediately detonate, destroying whatever it is attached to.
This assumes a ludicrously massive amount of available energy, but as some answers are already talking about accelerating large objects to sizeable fractions of c I figured I'd throw it in. You could single out an enemy ship with several grapples and then pump a short but massive burst of energy into it's shield - it would either detonate the ship or one of the enemy fleet's kinetic nodes, whichever one has the physically smallest grav generator. Either way it's a win. (Assuming some kind of safety mechanism which shuts down the generator before this happens this will still disable the enemy shield)
All of the above assumes access to virtually unlimited power generation. If such massive amounts of energy are not in play then a simple saturation attack will defeat any shield. This is the same principle as real-world missile defence saturation. All you need to know is the maximum energy output of the enemy shield and to pump more than this amount of energy into the shield. With a gravity shield this just means throwing enough objects at the ship to overwhelm the shield - this can't be an arbitrarily large number (for arbitrarily large amounts of energy the above singularity detonation scenario is where I ended up).