I can think of a few ways:
Stream of small black holes, that could eat up the sun slowly from the inside by bouncing around inside it. [@Forest's interest pushed me to calculate this: to avoid evaporating before reaching the sun when fired at light speed, each would need a Schwarzchild radius larger than 2*10^-21m (~one millionth of an electron's classical radius), giving a mass larger than 1.8 million kg. At that speed it'd reach the sun with a little mass left over after 8 minutes: but time goes up with the cube of the mass, and the radius goes up linearly with mass, so you can drop the velocity to reasonable levels without adding much size... but you're already handwaving away the creation of black holes, so adding in silly velocities seems almost trivial... This all assumes normal 3D spacetime, that relativity works on small scales, that Hawking radiation is a thing, etc.]
A one-dimensional singularity string, rather than a series of black holes.
Some mechanism to cover the sun in sunspots and hence darken it significantly.
Some mechanism to block out the sun, by placing something at an orbit that would block most of the sun, most of the time, from most of the earth.
None of these work in a "hard-scifi" setting, but could be OK in a soft scifi one.
Edit: OK, just realized another problem with the black hole thing. We need them to hit the sun's surface at below the escape velocity from the sun, or they'll just fly through and come out the other side, never to be seen again. So we can't just handwave and say "8 minutes, going at light speed".
We need to figure out the correct upper bound for the speed to fire from earth, to get them to arrive at 618km/s velocity needed to remain within the sun's gravity.
And let's say we want to not hit the Earth with these black holes, too. That means we need a velocity lower than needed to get from the sun to Earth. Kinda hard, if you're firing something from Earth. Then you have to fire the stream from a sol-stationary satellite, backwards along earth's orbital path at exactly our orbital velocity, so the holes fall under gravity towards the sun. You can handwave that you can fire it from the planet's surface facing the sun, too, since the holes should be slowed at least a LITTLE by passing through the sun.
You need to do this at Earth's point of closest approach, perihelion, about 147.5 million km away from the Sun.
Now we need to know how long it would take to fall that 147.5 Gm down the sun's gravity well.Thankfully, smarter people than I have done the math (http://curious.astro.cornell.edu/39-our-solar-system/the-earth/other-catastrophes/57-how-long-would-it-take-the-earth-to-fall-into-the-sun-intermediate) and come up with "65 days".
65 days is rather more than 8 minutes, so we need bigger black holes.
Now here, I'm just trusting some random guy on the internet (https://www.quora.com/How-fast-do-black-holes-evaporate/answer/Henry-Norman-3) for the equation, but I'm fine with that since the answers it gives seem in vaguely the right ballpark and I'm sure people will shout at me if we're wrong.
EvaporationTime = 5120 * pi * gravitationalConstant^2 * mass^3/(reducedPlanckConstant * lightSpeed ^ 4)
...where everything is in SI units.
Now, we want the mass, so we can rearrange that to get:
mass = CubeRoot((EvaporationTime * reducedPlanckConstant * lightSpeed ^ 4) / (5120 * pi * gravitationalConstant^2))
Assuming I didn't cock that up, we can plug in all the values we know:
mass = PrincipalCubeRoot((65*24*60*60 seconds * reducedPlanckConstant * (lightSpeed ^ 4)) / (5120 * pi * (gravitationalConstant^2)))
We slap that into Wolfram Alpha, and get: 4.057×10^7 kg
To figure the Schwarzchild radius, via https://en.wikipedia.org/wiki/Schwarzschild_radius, we use:
radius = 2 * GravitationalConstant * Mass / (lightSpeed^2)
= 2 * 4.057 * 10^7 kg * GravitationalConstant / (lightSpeed^2)
= 6.025×10^-20 meters
So, 30 times larger than the radius we could get away with at light speed, but still about 1/50,000th of the size of an electron radius. Pretty small.
There remain unanswered questions.
The first such question, of course, is... would these black holes have ANY effect on the sun? Or would they just, given their insignificant size, just zip right through it, and oscillate through in an "orbit" with a 260 day cycle and a radius of about 1AU?
And this, I don't have an answer to. I don't know how to begin calculating how wide of an area these black holes could pull in particles from in its path at those velocities.
Because, to do actual damage to the sun, we need each black hole to be large enough when it hits the sun that it will absorb more mass from its path through the sun, than the mass evaporated in the following 130 days before it returns to the sun again.
And we also need to calculate how MUCH damage it will do on each pass. This will increase each time, as the hole becomes more massive. Intuitively, I feel it should get exponentially worse, gobbling up more and more sun each pass through, perhaps doubling the damage each time, but I don't know that's the case, or whether it would take forever for it to eat away the sun a few atoms at a time.