He married Thursday (LNAB?), she died before him, before 1910.
Sources
"United States Census, 1850," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MH5W-8PJ : 4 April 2020), Peter Osborne in household of William Osborne, Randolph county, Randolph, Alabama, United States; citing family 850, NARA microfilm publication M432 (Washington, D.C.: National Archives and Records Administration, n.d.).
"United States Census, 1880," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M4V8-FCZ : 26 August 2017), Peter M Osburn, Roanoke, Randolph, Alabama, United States; citing enumeration district ED 113, sheet 364D, NARA microfilm publication T9 (Washington, D.C.: National Archives and Records Administration, n.d.), FHL microfilm 1,254,030.
"United States Census, 1900," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:M9Z1-65W : accessed 12 September 2020), Peter M Osborne, Precinct 7 Lanette Lanette town, Chambers, Alabama, United States; citing enumeration district (ED) 9, sheet 2A, family 18, NARA microfilm publication T623 (Washington, D.C.: National Archives and Records Administration, 1972.); FHL microfilm 1,240,006.
"United States Census, 1910," database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:MK3Y-C6D : accessed 12 September 2020), Peter Osburn in household of William L Osburn, Langdale, Shawmut and River View, Chambers, Alabama, United States; citing enumeration district (ED) ED 35, sheet 3A, family 52, NARA microfilm publication T624 (Washington D.C.: National Archives and Records Administration, 1982), roll 5; FHL microfilm 1,374,018.