Taiping diplomatic history can broadly be divided into about four phases:

1. 1851-53: The Taiping are somewhat known to Westerners, but have no direct contact.

2. 1853-54: Western powers attempt to make diplomatic contact but are rebuffed.

3. 1855-59: Very limited contact between the two, with both sets of powers primarily occupied in their wars with the Qing.

4. 1860-64: The Taiping attempt to make diplomatic contact but are rebuffed.

I've covered such broad trends, albeit periodised a little differently, in these two past answers:

• Did any country recognise the Taiping Heavenly Kingdom?

• Did the Taiping Heavenly Kingdom seek recognition as a separate nation from Qing China? Did it try to gain foreign recognition?

You may also find this post I wrote on Issachar J. Roberts, covering a very specific aspect of Taiping foreign policy, to be of interest.

But do feel free to ask if you have any more specific questions, as I do actually have many if not all of the sources for the 1853-4 diplomatic missions to hand and can elaborate further on them.