Two Indian birds make nests which hang from the branches of trees or bushes. These two birds are :

The correct answer is Sun-bird and Tailor bird.

Let us understand the nesting habits of the birds mentioned in the options to arrive at the solution step-by-step:

1. Sunbird: The sunbird builds a small nest that hangs down from the branch of a small tree or a bush. The nest is beautifully woven with hair, grass, thin twigs, dry leaves, cotton wool, bits of tree bark, and spider webs.

2. Tailor bird: The tailor bird uses its sharp beak to stitch together two leaves on a bush or tree to make its nest. It lays its eggs in the fold of the leaf that it has made. Since it crafts its nest hanging from bushes or tree foliage, it falls under the category of birds making hanging/suspended nests on branches or bushes.

3. Indian Robin: The Indian Robin makes its nest on the ground, between stones, or in low vegetation/roots, rather than making a hanging nest high on branches.

4. Barbet: The Barbet (Coppersmith barbet) makes its nest in a hole/cavity inside a tree trunk.

Therefore, out of the given pairs, the two birds that build nests hanging from the branches of trees or bushes are the Sun-bird and Tailor bird.