Puree strawberries and half the yogurt, then repeat with loquats and remaining yogurt in a separate container. (This works best if you have an immersion blender.)
Add honey to taste, then pour purees into popsicle molds in alternating layers. Run a chopstick or skewer through the molds to create a somewhat marbled effect, if you like.
Freeze at least four hours. Hold molds under running water to help loosen the popsicle, if you have trouble removing it.