Creating a homemade natural sunscreen without zinc oxide can be a bit challenging, as zinc oxide is one of the most effective and widely used natural mineral sunscreens. However, it is still possible to make a sunscreen using other natural ingredients that provide some level of sun protection.

Please keep in mind that the effectiveness of homemade sunscreens may not be as reliable as commercially available ones, and they may not provide sufficient protection against harmful UVA and UVB rays. It's always recommended to use a commercially tested and approved sunscreen for optimal protection.

That being said, here's a recipe for a homemade natural sunscreen without zinc oxide:

Ingredients:
- 1/4 cup coconut oil
- 1/4 cup shea butter
- 1/4 cup avocado oil
- 2 tablespoons carrot seed oil
- 1 tablespoon red raspberry seed oil
- 1 tablespoon non-nano titanium dioxide (optional)
- 10 drops of essential oil (such as lavender or chamomile, for fragrance)

Instructions:
1. In a double boiler or a heat-safe bowl placed over a pot of simmering water, melt the coconut oil, shea butter, and avocado oil together until fully combined.
2. Remove from heat and let the mixture cool for a few minutes.
3. Add the carrot seed oil, red raspberry seed oil, and essential oil to the mixture. Stir well.
4. If desired, add non-nano titanium dioxide for additional sun protection. Note that this ingredient may leave a white cast on the skin.
5. Once the mixture has cooled and slightly thickened, transfer it to a clean, airtight container.
6. Store in a cool, dry place. Use within a few months.

Remember, this homemade sunscreen may not have a high SPF value, and its effectiveness may vary. It's essential to apply it generously and reapply frequently, especially after swimming or sweating.

For optimal sun protection, it's always recommended to choose a commercially available sunscreen with broad-spectrum protection and an SPF of 30 or higher.