we move citrus about year around, the best time is early spring after the trees are about to break dormancy and regain active growth, but you shouldn't have any problems transplanting in other seasons of the year, just make sure your new location is prepared correctly.
What type of "black stuff" is this?.... Mold? Bird Poo? Roofing Tar?...

`Black stuff` on the leaves is most often sooty mould, not a problem apart from looking bad, but it does show there is a problem usualy either scale or aphids on the tree, ants climb up the tree and move the aphids/scale around and they leave a residue everywere they go, this goes mouldy
You need to keep ants from going up the tree with a band of grease or tar and then check for whats living on the tree and kill it, once its gone the mould will go, you can wash it off but best to sort the problem

If i find anything on a tree i tend to soak it with dilute neem oil , then followed by malathion and dipel , this lot usualy kills anything on the tree

Most people go for just something like the neem oil as it works for most things that crawl around on a citrus

Kim, I agree that your citrus most likely have a nice little infestation of scale insects, or maybe aphids. Or both! The excretions from either of those insects will support the growth of what we call (as mentioned above) Black Sooty Mold. Thus, it's not the black stuff that's the problem, but the insects. Ants may or may not take an interest in your infestation, so I wouldn't use them as an indication of a problem.

Transplant your trees now . It is the perfect time on the South .
Do not plant too deeply . Dig the holes wider rather than deeper .
Remove all fruit to allow the roots to recover and re-grow .
Do not fertilize until March .
Do not mulch .
Water every day unless you get rain .
Using a hose end sprayer , add a tablespoon of cheap dishwashing soap to the container and spray the heck out of all your trees - getting them nice and soapy . Do not use Dawn dishwashing liquid . Spray top , bottom and undersides of all leaves and trunks . Do not rinse . Re-apply in two weeks if needed . You can safely use soapy solution as often as you want on almost any plant .
No reason to use malathion and dipel . You will be eating the fruit from these trees eventually . Try soapy spray and/or ultra fine horticultural oils . Volck oil and Neem oil used to be used at full strength but the ultra fine is now preferred .
Good luck !

i want to move my lemon tree to another part of the yard to make room for a patio. my tree is full of lemons nor do i want to kill my tree its about 8 years old and bears well. how and when can i move it safeley?