This name is a synonym of Crataegus coleae Sarg..
The record derives from RJP
(data supplied on 2011-10-18)
which reports it as a synonym (record 5125) with original publication details: ; 1906 51 1906.
This name record (from RJP) was not included in version 1 of The Plant List. It is possible the same name was included from a different data source, to check this you can search for Crataegus eatoniana in version 1 of The Plant List.