The Lagerstroemia indica,would fit perfectly into your courtyard.

Mop Top Robinia. Formal and very pretty. More like a Ball on a Stick than an umbrella though.

I would avoid Robinias in a small backyard as they often sucker as they get older. They have a very vigorous root system.

Lukes suggestion is good. Another worth considering is Chinese Tallow tree (Sapium sebiferum). All of these will grow more than 4 meters. It is impossible to find a tree that will grow to 4 meters in a reasonable length of time and stop there.

Hiya

I am looking for a small shade tree that is deciduous too. I have also considered crepe myrtle and chinese tallow. The former can look a bit sparse but the flowers are gorgeous. The chinese tallow is becoming extremely common around Perth as a street tree - it has a very nice growth habit and the leaves do turn colour at the change of seasons - but it does get larger than 4 m

Have you thought of an almond tree? My neighbour's almond is about 5 m and has a spreading shape. It does need pruning however to keep in shape. Another option we are thinking of is a white mulberry - the neighbour across the road has it trimmed at a neat 4 m. Another option is a blossom tree (plum or flowering peach).

We still can't decide. Good luck.

Aggie

an Albizzia julibrissin (aka Persian silk tree) is an option worth considering, it is a short(in comparison to many others) spreading tree - it has feathery soft foliage similar to a jacaranda(bipinnate leaves) for lovely dappled shade and small pink flowers that look like silky tufts or puffballs. These trees are quite hardy

The chinese tallow always looks lovely and colours well in Autumn even in warmer areas. It takes many years for them to grow to 4 metres, but yes they do grow bigger. What about a tibouchina - beautiful purple flowers in Autumn or go with the Port Wine Magnolia.

If you have a courtyard situation and can't decide upon a tree, what about changing the outlook by planting say jasmine along the walls and add a (Jamie Durie would approve) water feature.

Firegirl

Try the Arapaho Crepe Myrtle. They thrive in sunlight and depending on the intensity of sunlight they give deep red blooms.

They grow 3-5 ft. per year.

The White Flowering Dogwood Tree is another beautiful tree that grows in a spreading canopy. The blossoms are creamy white in the spring and the leaves turn scarlet in the fall. Check this link for small shade tree ideas:

http://www.fast-growing-trees.com/ShadeTrees.htm

lol

Have a look at Hymenosporum flavum (Native Frangipani)
Grows from Adelaide to Cairns+. Colour ranges from Pinks through to gold with red centres shown here http://asgap.org.au/APOL2006/jul06-s2.html
As they get older they spread in a beautiful umbrella.
HTH. Nat.