I have found the family on the 1901 Census - indexed as Bryom.
Ecclefechan, Hoddom, Dumfriesshire
James Bryom 37 General Labourer b. Hoddom, Dumf.
Jane Ann Bryom 37 b. Portsoy, Banffshire
Isabella Bryom 14 b. Hoddom
John Bryom 13 b. Hoddom
Janet Bryom 11 b. Hoddom
Agnes Bryom 11 (twins??) b. Hoddom
Jane Bryom 9 b. Ireland
Christina Bryom 7 b. Ireland
James Bryom 6 b. Ireland
Robert Bryom 3 b. Hoddom
George Bryom 1 b. Hoddom
So, the reason you can't find Christina's birth is because she was actually born in Ireland - this is obviously why we can't find them on 1891 Census either. Around 1890/91 the family went to Ireland and returned to Hoddom around 1897/8.
I found out the same information re. Jane Ann Christie as has been mentioned already but did find her with family on 1871 Census - indexed as Chrisley
1871 Census - 8 Keithhall Road, Inverurie, Aberdeenshire
James 35 Farm Servant Unemployed b. Chapel, Aberdeenshire
Isabella 34 b. Cullen, Banffshire
Jane 8 b. Portsoy, Dumf.
James 6 b. Inverurie
Christiana 4 ditto
Isabella 3 ditto
Mary 1 ditto
Annette