If you improve the structure of your soil you could plant almost anything in your garden. I would recommend digging a soil conditioner, peat, compost and gypsum (all available from garden centres) through your soil to improve its structure.
The soil conditioner will adjust the condition of your clay and mean you could plant any of the annuals or perennials available at Awapuni Nurseries. Remember, when you replant your annuals you will need to re-condition your soil.