Even though the names are in the Church Parish Register, they are most likely to be buried in Ruthin Road graveyard.
The Ruabon Road cemetery opened in 1876 and all "new" plots were opened there , Ruthin Road was still used for a few years for existing plot owners.
You said you've been to Ruabon Road, I did a quick search and found quite a few Mulligans, and then did a Grave number search which found a few more that were spelt differently.
There are also a few "strays" . grave number is the last, so I`ve grouped them together.
MULLIGAN THOMAS age 80 WORKHOUSE 355 11/10/1882 00843
MULLIGAN JOHN age 51 BELLE VUE ROAD 756 11/05/1887 00843
MULLIGAN MARY ELIZABETH age 15M 2 JONES' COURT, MOUNT STREET 7593 21/01/1911 00843
MILLIGAN MARY age 82 4 BELLE VUE 10297 28/03/1917 00843
MALLIGAN PATRICK age 75 CROESNEWYDD HOSPITAL 17437 07/06/1939 00843
WILLIAMS JOAN age 47 12 BRYN OFFA WREXHAM 32156 16/07/1979 00843
MULLIGAN MICHAEL age 50 BELLVIEW ROAD 549 03/02/1885 00840
MULLIGAN ELIZABETH age 69 PIERCES SQ,PENTREFELIN 6575 09/11/1907 00840
PENKETH JOHN GEORGE age 85 NAZARETH HOUSE 32177 24/08/1979 00840
MULLIGAN MARY age 53 5 JONES COURT MOUNT STREET 12376 26/12/1923 00669
MULLIGAN ANN NORAH age 29 13 ALBERT ST WREXHAM 15764 01/11/1934 00669
MILLIGAN THOMAS age 72 21 CLWYD WEN WREXHAM 20310 02/07/1946 00669
CLUTTON JOHN WILLIAM age 5 13 BANK ST,SOUTHSEA 6619 03/01/1908 00669
PRILE NELLIE age 77 9 THE LAURELS ACTON WXM 31703 25/07/1977 00669
PRILE JAMES PETER age 80 MAELOR GENERAL HOSPITAL 32165 30/07/1979 00669
MULLINGAN PATRICK age 72 CROESNEWYDD HOSPITAL 17245 24/12/1938 09883
MULLIGAN JOHN age 61 MAELOR HOSPITAL WREXHAM 27252 17/07/1963 09883