Deck cup holder options: tables, clamps and portable bases
Choose the support you need without assuming every rail is a mounting point.

A stable side table
A table can add both drink space and room for a book. Check height and reach from the actual chair before choosing.
Railing or chair mounts
Use only an accessory intended for the exact mounting surface. Check its instructions, fit and whether it obstructs movement. No-drill does not mean universal fit.
A portable base
Steadi works with compatible drinkware on a level, supported spot. It is freestanding and does not attach to the deck, table or rail.
Choose by the real problem
If you have no usable surface, a base alone will not create one. If you have a suitable surface and want a wider resting base, check your drink and the 5.2-inch footprint.