To "First World Problems"
For the original question
* Not a recliner, but for helping your back similar to how an exercise ball does but with more support for long coding, I have used a "SwingSeat" at my desk for a decade or more (http://www.swingseat.com/). This was good enough to get me by until the last round of surgery (which was actually a success) made it too hard to sit upright all day.
* A "Zero G" chair, like the ones by Human Touch (I use a Human Touch Perfect Chair), a bit pricey but not awful. Combined with a laptop table that can raise and angle the laptop you can actually do the vast majority of your work from a completely reclined position.
* For a desk, rather than reclining all the time, I assembled a custom desk from Anthro using their Console line that has a tray that can raise and pivot from sitting to reclining (which actually needs to be raised higher than sitting) to standing (great for those of you who don't have partial leg paralysis, good for me on rare occasions). The desk is HUGE but dang, it does everything. It is the Console with full pole extensions bringing it to almost 6' with monitors on a shelf 8" higher than the shelf that hosts the keyboard tray. Which means the monitors can raise up to standing position as well. I can, if I use a trackpad to avoid mouse problems, use this in combination with the Perfect Chair as a rigged solution similar to the next one.
* I couldn't afford this, or at least I could have before I needed it, but can't now. But if you can, the desks from ErgoQuest are perfect. And some of them are inexpensive enough to be not tooooo awful on the budget (if I had the money I spent on the SwingSeat, Anthro Console and Perfect Chair I could afford an ErgoQuest). You can -sometimes- find these on Ebay but not usually from someone willing to ship and often not for significantly less than having the right one built to your specs.