He is married to Irmgard von Rott.
They got married
KUNO (-[1110] or after). Berthold's Chronicon of Zwiefalten names (in order) "Ottonem comitem, Counonem Horburgensem, Burchardum episcopum Traioctensem, Bertholdo" as children of "Counoni comiti de Lechisimundi" and his wife "Mahtilt soror Liutoldi comitis"[1354]. 1083/1103. Graf von Horburg. Wegener cites a donation to Hirsau dated [1110] by Kuno and his son Konrad[1355]. m (after [1085]) as her second husband, IRMGARD von Rott, widow of GEBHARD [II] Graf von Sulzbach, daughter of KUNO [I] von Rott Pfalzgraf von Bayern & his wife Uta --- (-14 Jun [1101], bur Kastl). The argumentation for this second marriage of Irmgard is complex. The Fundatio Monasterii Berchtesgadensis refers to her second marriage after "patre comitis Perengarii defuncto" but does not name her second husband[1356]. Irmgard's second husband was presumably the father of "fratris sui Cunonis de Horburc" who is named in the same source as co-founder of the monastery with his brother Berengar Graf von Sulzbach. The necrology of Baumburg records the death "XVII Kal Jul" of "Irengardis com de Sultzpach sor na"[1357], which suggests that she was still the widowed "Gräfin von Sulzbach" when she died. If this is correct, her other husband must have been Heinrich von Lechsgemünd, supposed brother of Kuno, who was killed in battle in 1078 (see above). This is the marriage proposed by Wegener[1358], although he does not go through the present argumentation in reaching his conclusion. It would, however, contradict the explicit, although incomplete, statement in the Fundatio concerning Irmgard's marriage after the death of Graf Berengar's father. Another probably relevant factor is the fact that "Cunonis de Horburc" is named in the Fundatio after his brother Berengar, which suggests that Kuno was the junior partner in the foundation and also the younger brother. Until further information comes to light, it is assumed that Irmgard's Lechsgemünd marriage was her second, and that her husband was therefore Kuno von Horburg. The Baumburg necrology entry must be explained either because Irmgard had separated from her second husband before her death, reviving her previous title, or because the compiler of the necrology considered her first husband of more importance than her second and referred to her by his name.
Graf Kuno & his wife had two children:
KUNO von Horburg (-30 Jun [1138/39]).
KONRAD (-murdered near Dachau [1128]).
Bronnen:
[1354] Bertholdi, Zwifaltensis Chronicon 19, MGH SS X, p. 106.
[1355] Codex Hirsaugiensis fol 39b, cited in Wegener (1965/67), p. 258.
[1356] Fundatio Monasterii Berchtesgadensis, MGH SS XV 2, p. 1065.
[1357] Necrologium Baumburgense, Salzburg Necrologies, p. 236.
[1358] Wegener (1965/67), p. 259.
https://fmg.ac/Projects/MedLands/BAVARIAN%20NOBILITY.htm#KunoHorburg10831103