Yes, you can definitely dye curly hair. However, it's important to take some precautions and follow specific steps to ensure that your curls stay healthy and the color turns out as desired. Here are some tips for dyeing curly hair:

1. Deep Condition: Before coloring, deep condition your hair a week or two in advance. Curly hair is prone to dryness, and conditioning helps to moisturize and strengthen the hair, reducing damage from the dye.
2. Do a Strand Test: Always perform a patch test to check for any allergic reactions and to see how the color will look on your hair.
3. Choose the Right Product: Opt for hair dyes that are ammonia-free or have low levels of peroxide, as these are gentler on curly hair. Look for products specifically formulated for curly or dry hair.
4. Use a Color-Depositing Conditioner or Gloss: If you're hesitant about full-on dyeing, consider using a semi-permanent color or a color-depositing conditioner. These are less damaging and can enhance your natural color.
5. Section Your Hair: Divide your hair into small sections to ensure even distribution of the dye and to make the process more manageable.
6. Apply with Care: Apply the dye starting from the ends and working your way up to the roots. This technique reduces the risk of over-processing the fragile ends.
7. Moisturize and Nourish Post-Dye: After dyeing, use a sulfate-free shampoo and a deeply moisturizing conditioner to keep your curls hydrated and minimize color fade.
8. Regular Maintenance: Continue with a consistent deep conditioning routine to keep your curls healthy and the color vibrant.

Remember, curly hair can be more delicate due to its structure, so taking extra care during and after the dyeing process is crucial to maintain its health and appearance. If you're unsure about doing it yourself, consulting a professional stylist who specializes in curly hair can also be a great option.