Currently using pushpins but I’d like to make it more functional.
There are several solutions for this. You can buy ceiling rod holders and mount the curtain rods to ceiling. You can also DIY it with PVC pipe. I have attached a HOMETALK link to a bed canopy, but, the principle would be the same with your situation.
Whichever hardware you choose to go with to support the fabric, make sure that you mount it directly into the ceiling 2x4's rather than simply into the ceiling tiles or sheetrock. Otherwise every time you go to tug on the curtains, the motion will eventually lead to pulling out the whole lot. You will then have a bigger problem with large holes to patch up.
It is less invasive if you use a wire mount. Lowe’s and Home Depot stell the set with the hardware, ikea also has a similar solution... It is a wire that comes with two large screwhead anchors. Hang the fabric or curtain with curtain clips (some kits provide clips). Good luck.
They have mentioned the clips to hang the curtains with, but you can also use the cheapo shower curtain clips. They work like a charm. Especially if you are hanging on wire. They don't get hung up like the plastic ones tended to.
Use a spring (such as used in old fashioned screen doors) and slide curtains on as you would on a curtain rod. You can slide them aside.
The good thing is that you can put them very close to the ceiling and have no space between curtain and ceiling.