Armchair drink base or arm tray?
Compare separate support with furniture attachment.

An arm tray
A tray must suit the width, curvature and material of the arm. Check its support rather than assuming all upholstered arms are alike.
A side table
A separate table avoids loading the arm. Its height and stability matter as much as how close it sits.
Steadi
A compatible container gains a wider base without attaching to the chair. It still needs a level supported surface.