Answer: Could you be referring to Portulaca, or "moss rose"? (I've never heard it called sun rose before though.) Portulaca is a common vining plant, with thick, narrow leaves and lovely flowers--the flowers look more rose-like than dandelion-like, though they do come in yellow.
If it is indeed portulaca, then here's the technique: harvest the seed when the seed capsule is dry, but vefore it shatters and releases the seeds. Shake the tiny seeds out, and let them dry for several days if you plan to store them. Sow the seeds in peat pots, since they resist transplanting. Don't cover the seeds with soil, but simply press them into the soil surface. The seeds need light to germinate. Maintain at a temp of 68-86 until germination, which can take two to three weeks or more.
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