I followed this recipe for low-carb lemon poppy seed muffins. I only substituted coconut for almond flour and granulated monk fruit for splenda. The mix was really loose and dry when I put it in the tins. I baked it for the max specified 20 minutes and they didn't rise (I didn't swap baking soda for powder, like some do). If I want to make these again, what do I modify to get these muffins to look like actual muffins?
Your recipe has no gluten in it. Baked goods without gluten tend to have a crumbly texture; muffin batter usually contains at least some wheat flour, which contributes gluten toward the muffin's structure. The Kitchn has a good blog post about using vital wheat gluten, which can be added to a recipe that is in need of a more bread-like structure (assuming no dietary restriction on gluten). If you add too much, you'll have to adjust the other ingredients in the recipe to compensate (mainly liquids, but possibly fats as well) but a little goes a long way; for your recipe, one tablespoon might be a good starting point.
Vital wheat gluten does contain similar carbohydrates to those found in regular wheat flour, but much less; where regular flour is almost entirely carbohydrates, vital wheat gluten is mostly protein. Consult the nutrition info before you buy it if you're worried about adding carbs to your recipe.
Adding gluten can also affect how the muffin rises, so you might find that's enough on its own; but it's not directly a leavening agent. More good info here: What does gluten "do" in baking?
Coconut flour really soaks up moisture, so it can't just be substituted for other flours. You should use a coconut flour recipe, but if you can't find a coconut flour recipe for what you want to bake you need to (approximately) double the liquid in the recipe.