Hi Gavin,
These are from an old burial index I have. Can't remember where I got it from. As you can see there isn't many Stewarts in this one but I will look in the other index too. 
3114   Stewart   John   ng   ng   1717-02-14   1717-02-15   Newbattle   Mortcloth £2
3115   Stewart   John   ng   Gibraltar   1811-01-ng   1811-01-09   Newbattle   Mortcloth 10/3d
3116   Stewart   ng   ng   Blackcot   1818-03-ng   1818-03-30   Newbattle   Child of Thomas Stewart, mortcloth 1/3d
3117   Stewart   M.   75   Bonnyrigg, Cockpen   1842-03-03   1842-03-07   Newbattle   Informant, John Romans, friend, dropsy
3118   Stewart   Elizabeth   75   Newbattle, Newbattle   1844-02-19   1844-02-23   Newbattle   Informant, William Oliver, son
3119   Stewart   Margaret   9   Eldindean, Lasswade   1848-08-14   1848-08-17   Newbattle   Informant, James Stewart, father, fever
3120   Stewart   Thomas   20m   Eldindean, Lasswade   1848-10-29   1848-10-31   Newbattle   Informant, James Stewart, father, decline
3121   Stewart   Lewis   2   Brewer's Bush, Cockpen   1852-05-09   1852-05-10   Newbattle   Informant, Lewis Stewart, father, measles
3146   Stuart   ng   ng   Easthouses, Newbattle   1761-05-16   1761-05-17   Newbattle   Child of Janet Stuart, decay
3147   Stuart   Janet   ng   ng   1770-05-ng   1770-05-29   Newbattle   Coffin 5/-
3148   Stuart   ng   ng   ng   1781-03-ng   1781-03-25   Newbattle   Child of James Stuart, mortcloth 1/3d
3149   Stuart   ng   ng   ng   1794-01-ng   1794-01-19   Newbattle   Child of Charles Stuart, mortcloth 1/3d
3150   Stuart   ng   ng   ng   1796-10-ng   1796-10-02   Newbattle   Child of James Stuart, mortcloth 1/3d
3151   Stuart   ng   ng   ng   1798-10-ng   1798-10-28   Newbattle   Child of Chson Stuart, mortcloth 1/3d
3152   Stuer or Stuart   ng   ng   Newbattle   1763-07-26   1763-07-27   Newbattle   Child of John Stuart, drug (dreig) pox
I visited the Newbattle Old Cemetery recently, but without being able to find my family plot and headstone. I wrote to Midlothian Council who replied with a copy of the layout by plots. I've attached a PDF file of the layout to help people potential locate plots if you know the plot number.
When I visited Newbattle and Lasswade I took some random pictures, uploaded then to find-a-grave with a little research. I also found out about neighbouring plots to my James Stewart and have added them also with some research. I hope to revisit and take much much more pictures and upload them to Find a Grave which I use because it freely available with minimal ads and easy to use.
I am still trying to see if any other of my Stewart Family are in this cemetery. 
My unaccounted for Family
Jane Stewart (b.1839 Penicuik) entry in 1841 census (suspect died before 1851)
Marion Stewart (b.abt 1841 Lasswade - 1913 Colinton, Edinburgh) married James McDougal
James Stewart (b.1843 Newton Village) entry in 1851 census only
Janet Stewart (b.abt 1845 Lasswade) entry in 1851 census only
William Stewart (b.abt 1848 Roslin) entry 1851 & 1861 only
Adam Stewart (b.abt 1850 Roslin - d.1925 Lasswade) married Helen Reid
Elizabeth Stewart (b.abt 1853 Lasswade) entry 1861 & 1881 only (married Griffin but not UK records)
Isabella Stewart (b.1856 Lasswade - 1887 Dalmeny, near Queensferry)
Margaret Stewart (b.1862 Lasswade) Suspect she married a John Murray Leishman both died at Errol
Jessie Williamina Stewart (b. 1866 Lasswade - d.1907 St George Edinburgh) spinster
Elizabeth Griffin nče Stewart is someone I really want to find out more about but have hit a road block. She had a daughter Eliza (1879 Stobhill - 1882 Borthwick) and a son Charles (1877 Stobhill - 1945 Edinburgh) he married a Isabella Adams.