Joanna
There are too many Morgans (often over 50 in one year) in the directories to list over that period, but below are those connected with the jewellery (in the broad sense) trade:
1868-80
Morgan Benjamin Manufacturer of tea caddies and card cases and general pearl worker. All kinds pearl, pearl flowers and ornaments always in stock, (listed as Morgans mill and no 63 different years), Macdonald St. Summer Lane. Home: Milton place, Victoria road. (this full description listed in only one year)
1883-4
Morgan Benjamin , pearl worker. 18 Frankfort St, Summer Lane
1888 (probably taken over from Benjamin, but address not listed 1890)
Morgan Charles, pearl worker, Morgan's mill, Frankfort street, Summer lane
1868
Morgan Thomas, pearl grinder, Bullocks Steam Mills, Cliveland st
1873
Morgan Joseph, pearl grinder, Thompsons mill, snow Hill, home :Geach St
1876
Morgan Arthur Joseph, watch maker. 67 High St Aston
1880
Morgan Arthur Joseph, watch maker. 113 Wills St, Hunters Lane
1888-1890
Morgan George, dealer in antiquities, 19 John Bright st
1892
Morgan Henry, antique'dealer, 11 Broad-Street corner
1896-7
Morgan Thomas, Pearl button maker, 30½ Barr street
1897-9
Morgan, Arthur, ring maker, 2 Warstone Parade East
There is also;
Morgan George, chaser, 29 Mary St (1876), 22 Caroline street(1878-84), 1A Caroline St (1888-92), 29 Mary st, Caroline st (1895-6). In 1897 a George Morgan is listed at 29 Mary St and 20 Caroline St (one possibly a son?). In 1899-1900 it is just no 20 Caroline St. He/they not listed as Jewellery trade, but in jewellery quarter, so probably in that trade.
In 1899-1900 there is a Charles Morgan, second master at School of Art. Margaret Street, which I believe was involved a lot with the jewellery trade, among other arty things.
I have missed out a number that slightly possibly might be in jewellery trade (mount maker, brassfounder) and have only looked at 1868-1900. Can look outside this range if of interest to you.
mike