A network of Fresnel lenses could collect solar energy and reflect it all back onto the Sun's surface - perhaps at a few carefully chosen locations. The Sun floats in a vacuum, so the sudden superheating of spots on its surface might create supersonic shock waves that travel inward towards the core, causing an implosion. If sufficient amounts of the Sun's own energy is reflected back onto itself it might implode the Sun and create a neutron star. A beacon would consist of controlling the beams from the neutron star, so the pulse that ETs detect would carry information.

Another idea, is to use powerful sunbeams to 'excite' the atmosphere of Jupiter. ET would know the mass from the orbit period and distance, and so Jupiter could not be a source of fusion radiation - it's not massive enough. It must be artificial. They would then waste centuries of time trying to figure out WHY we would do this, and imagining that we must be super-advanced technologically, and have a purpose far beyond merely creating a beacon for them to detect. Since they wouldn't be able to figure it out, humans must surely be far superior to them! lol.