If your brackets are going just next to the window frame, the sheet rock there would be over a stud. Drill first before you put the screws in.
Command hooks or tension rods.
Outdoor command hooks work great. You can even use a drapery rod with them because they hold a lot of weight. You can paint them to match the color of your walls too.
There is usually a decent lintel above windows. However, if the sheet rock was installed on battens, leaving a decent gap behind them, you might consider fixing a decorative batten of wood across the top, you can then screw the curtain rail to this wood. if you want to go into the sheet rock, my favourite for holding plenty of weight is the butterfly bolt/spring toggle. Ok, this involves making a larger hole but those spring toggles open up inside the cavity and fix brackets really securely
Thank you all for your ideas.
You could try a tension rod on the inside of the window frame.
Here's a great post with some tips.