here I can answer as a sporter ;)
Your problem is twofold:
- Your range of motion is limited, and
- your core is not strong enough
To address 1. you can do stretching, common gymnastics stretching: Guide to basic stretching. Yoga is also a good option but I consider common stretching more to the point (and you will need that for yoga too, anyway).
For 2. there is no easy answer: You need to strengthen your core. Please note that for many Japanese, Koreans and Indians the lotus position is easy because they use to sit on the ground, this has a huge impact on the core muscles: Our western chairs hold our backs and void us from using too much force for sitting, making that our cores are less strong, specially a large amount of small muscles...
There are two basic exercises that you can do for that: the plank and the bridge: 10 core workouts
For both, the core exercises and the stretches you can start holding them for 20 seconds, build up to 30 seconds and then up to 1 min and 1:30, there is a maximum of 90 seconds (1:30) above which there is no effect. I fact the proper stretching reflex of the muscles is triggered after 20-30 seconds after which they elongate.
Other things that you may do are:
- Stand as much as you can: If you drive by train don't sit. If you are in public spaces try avoid sitting and stand instead.
- Use the stairs not the escalators/mechanic stairs.
- Give sitting on the ground a try, even when not for meditation
So, here's my grain of salt. I'm not a Buddhist, mind you, I practised Zen a lot of years ago, but I recall zazen being very painful to hold while now I can sit comfortably in the lotus position or seiza (the real one, as in Kendo).