Hello Margaret
The document which I believe to be the origin of Evnlie is called The Littles of Galloway and the County of Kent
(not the English Kent 
) by Geo. E Little.
There is a copy of it - or part of it - at
www.donlittle.com/Family Tree/thelittles.htm
There is much more Little information at
www.donlittle.com There is a link to the above from it but the link appears to be currently broken.
You will see that the document refers to a marriage in 1746 between Janet Johnston of Crookholm and David Little of Evnlie. Crookholm is on 19th century maps and on modern; Evnlie appears on neither. However about i mile north west of Crookholm - and probably the next 'farm' - is Airnlee - which is on both modern maps and on 19th century maps. Both place are about 3 miles east of the 'town' of Canonbie.
The Dumfries and Galloway Family History Society has published a transcription of the memorials of Canonbie Parish Church. There are 579 in total of which 69 include the name Little. You may of course have used this as a source already.
No. 570 records the death of John Johnston of Earnlie (sic) in March 1780 age 77 years. Also his wife, his son - and Sarah Johnston of Glingerbeck-know.
I don't know if anything helps but I wonder whether I could go out on a limb and say for Evnlie read Ainlie

Perhaps I shouldn't.
Regards
Reiver