Reddit reviews AmazonBasics Curtain Rod Clip Rings for 1" Rod, Set of 7, Silver Nickel
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Set of 7 large clip rings in Nickel for hanging curtains from a curtain rodPlated-steel rings fit curtain rods up to 1-inch in diameter; each curtain ring can hold up to 3 poundsHeavy-duty spring-tension clips attach securely to top edge of curtainPerfect solution for curtains with pockets or tabs that are too small for curtain rodMatching AmazonBasics curtain rods, brackets, and holdbacks complete the look (sold separately)Each clip ring is inserted from the end of a curtain rodNote: This rings fits 1” or smaller diameter rod. The actual ring itself has two dimension – the inner diameter (1.26”) and the outer diameter (1.6”)
Your idea might work, but I would be concerned about the blackout curtains being much heavier than the sheer curtains. That might pull a bit on the lighter fabric.
This doesn't exactly answer your question, but have you considered layering the 2 curtains? Either on 2 separate rods or both sets on the same rod (sheer on the inside and blackout on the outside like this: https://i.pinimg.com/originals/9c/36/34/9c36341efed7189ef060637badc2afce.jpg). Sheer curtains are so pretty, and if you do end up lining them, it's going to look much heavier.
Or you could purchase clip rings and simply double up the sheer and blackout curtains. https://www.amazon.com/AmazonBasics-Curtain-Clip-Rings-Nickel/dp/B01N5B2MKA
Please disregard these suggestions if they doesn't work for your situation!