I too have the bad knees issue (long-term arthritis, etc.), but often have to assume the kneeling position while working on my back/shoulder flexibility. In that setting, I find I often have to switch from that position to cross-legged, which means I have to focus more on keeping my back straight the entire time. However, if you prefer kneeling/staying still without shifting/fidgeting for a prolonged period of time, and want to work on your stamina in that position, @skyrich made a great suggestion of keeping your knees apart so more of your weight is between your legs. You can even put a foam yoga block between your ankles so your tailbone has something to rest on besides your heels.
If you're more of a traditionalist (or your Dom is), and would rather keep your legs under you, you could try tilting your pelvis forward so that more of your weight is resting on the meatier part of your calves, instead of your ankles. The important nerves there are deeper (under the gastrocnemius (calf) muscle) and more cushioned compared to the superficial branches that supply your ankles/feet/toes. I also find it's easier to maintain better back/neck posture this way without getting those cricks/knots that we are all soooooo very fond of (she said sarcastically), and it puts less pressure on the knee joints as well. You can also take turns pointing your toes on each foot while kneeling, which will help engage the muscles in your calves and feet --> stimulated/enhanced blood flow to the vasculature around the nerves there, hopefully preventing the pins and needles but also being sneaky and subtle about it
I'm with @Sirsbabydoll, though: kneeling sucks.
PS: I would not recommend putting your ankles together while in this position. It puts too much torque on the knee joints, which will weaken the surrounding ligaments and make you more prone to tearing something.