Nanci, I've done abit of research on your Josiah W. Morton:
1880 census TX, Dallas Co, Lancaster pg 265d: 36/36 Morton JW age 56 Wagon Maker born SC father born: Ire mother born: Penn; Alva son age 30 born Tn; Rosa 24 Ms; Emma 21 born Smith Co Tx; Ella 18 born Smith Co Tx
1870 census Tx, Dallas Co Dallas pct 2 pg 333: Morton JW age 46 farmer born SC; Alva 19m Tn; Rosa 14f Ms; Frances 11f Tx; Ella B 8f Tx
1860 census Tx Smith Co, Garden Valley pg 32b: Morten JH age 36 born SC; Catherine 34 Tn; Martha 12 Tn; Henry 10 Tn; Mary 7 Ms; Rosa 4 Ms; Frances 1 Tx.
It appears the family was living in Tennessee during the 1850 census. I don't have access to any 1850 Tn indexes.
My Morton file does show John Morton & Jane Peden had a son James. I lost track of James after 1830 census Greenville Co SC. In the 1880 census Josiah reported his father was born in Ireland and mother in Penn. This is consistent with family lore about James Morton & his wife Mary Montgomery.
Hope this helps Bill Morrow House of Jane & House of Samuel SC Pedens