I feel your pain. I love garter belts but getting the clips on the stockings is always a frustrating challenge.
I was walking down the bedding aisle in Walmart one day and noticed some packages of bed sheet clips. A light bulb went off. I was in a hurry so didn’t buy them then and there, but later found them on Amazon in both white and black colors.
They work great! But a couple of caveats: they are a bit clunky, and while they easily and firmly attach to the stockings, you also need to wear something substantial for them to attach on the upper end. I often clip the upper ends to the bottom of a corset and they look great. They will also attach to the bottom of a camisole or bustier. I’m sure they would work with an actual garter belt but it would need to be a fairly thick one.
For a better look, I have painted the outside of my metal clips (the side that shows) in black or white to match the color of the strap.
Hope this helps!