What's the best way to hang a curtain rod without studs so it's secure

I would suggest a molly bolt if there are no studs. You still need to be careful about weight of rod and curtains even with a Molly bolt.

A tension style rod would solve that problem. But if you want to put on up that doesn't have that option use plastic u shaped cuts to set the rod in.

If your windows are deep set you can use a tension rod and hang the curtains inside the window frame

Wall anchors are all you need. Purchase ones that will hold the weight you intend to put on them. Typically 25# will work. Make sure the screw that comes with the anchors will go through the hole of your rod before you purchase. That way, not second trip to the store. Good luck.

Agreed. If the weight is too much, see if you can use some wood attached to the lintel to spread the weight.