I have a large garden, mixed native and exotic. There are some sheltered places, but we get frosts to -3 in winter.
Yes, you should be able to grow a coral tree. Your average low temperature is 50 degrees F (10 degrees C) and coral trees' hardiness goes to 25 degrees F (-4 C). You say you get freezes to -3 so it is close. So plant it where it will get some protection and be sure to mulch well.
My loved Ciral Tree has all its leaves going yellow, I live in Cyprus, I have been following advice re watering (not to do it!) and it is usually beautiful, this year only 1 little flower so far. help?
My first suspicion would be a pH imbalance.
Since these are, technically, legumes- They will harvest their own nitrogen. This means that feeding is completely unnecessary. This leaves pH in question. If it is too low, it will lock out phosphorus and potassium. This will affect flowering. When checking, it is best to keep the soil within a range of 5.5 to 7. These articles will help you to test your soil:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm
This article will give you more information on the care of the tree:
https://www.gardeningknowhow.com/ornamental/trees/coral-tree/coral-tree-information.htm
I have fed it with Dr. Earth flowering tree fertilizer but it still looks the same as when it was planted.
Unfortunately, your photo did not come through. I am unable to say what caused your problem. It sounds like it suffered from transplant shock. This article will help:
This article will help you with the care of the tree:
https://www.gardeningknowhow.com/ornamental/trees/coral-tree/coral-tree-information.htm
My Coral trees are constantly producing new growth but the older leaves turn yellow and drop off as fast as the new ones develop.
You are in the correct zone for growing coral trees so that is good. They may be overwatered. These trees need little water and no fertilizer. Try cutting back on water and see if that helps. Here is more care information:
https://www.gardeningknowhow.com/ornamental/trees/coral-tree/coral-tree-information.htm
This is a young Coral. My photo won’t upload.
This could be due to soil overfertility, or it could be actual disease. As a legume, these trees will feed themselves nitrogen harvested from the air. Too much nitrogen in soil will burn the new growth.
These articles will help you to test your soils:
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-moisture-in-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/test-soil-for-pests-and-diseases.htm
https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/making-sure-soil-drains-well.htm
This article will help you with the care of the tree:
https://www.gardeningknowhow.com/ornamental/trees/coral-tree/coral-tree-information.htm
I plantee the tree about 4 years ago. I protected with frost cover the first 3 years during the winter. It's growing taller every year and is full of leaves, yet it hasn't flowered once. What can I do to help thus beautiful tree to flower.
Make sure you are not overwatering. They need very little water and fertilizer. Mulching around the tree should give it ample nutrients as the mulch degrades. They also need full sun and well draining soil. A lack of sufficient sunlight can prevent flowering.
Here is more:
https://www.gardeningknowhow.com/ornamental/trees/coral-tree/coral-tree-information.htm