I use a [bottle cage](Two Fish The Quick Cage Water Bottle Holder Silver https://www.amazon.com/dp/B00P4ALJ7Y/ref=cm_sw_r_apan_glt_fabc_SJTC03HK7MKRSW1TMY4B). It won't hold a paper cup but it does hold lots of travel mugs, my favorites being the completely leakproof ones made by [contigo](Contigo Autoseal Transit Stainless Steel Travel Mug, 16 Oz, Stainless Steel with Blue https://www.amazon.com/dp/B0160LEYFY/ref=cm_sw_r_apan_glt_fabc_G89ER4ANCTQAYVSVFTB1).
I love my set up, it's spill proof and far more stable than a paper cup in most of the plastic cupholders made by medical manufacturers.