Here is a photo of modern Heidelberg, with Heidelberg Castle on the hill and the Old Bridge over the river Neckar. Founded in 1386, Heidelberg University is Germany's oldest and one of Europe's most reputable universities. This university was already 200 years old when the Coberstein's in these records were here.

Heidelberg records:

Here is the link for Eucharii Koberstein decendancy link in FamilySearchwhich includes all these records.

Michel Koberstein database in Ancestral Quest.

record title: Germany Marriages, 1558-1929 
groom's name: Michel Koberstein 
bride's name: Susanna Kleinschnitz 
marriage date: 09 May 1603 
marriage place: Heidelberg, Baden, Germany 
groom's father's name: Eucharii Koberstein 
bride's father's name: Niclas Kleinschnitz 
bride's marital status: Single 
indexing project (batch) number: M93414-2 
system origin: Germany-EASy 
source film number: 1189252 

It is a high probability this is the same as Michael Koberstein in the "euchariu" Koberstein line.  However the father in that line is Johannes, so he would have to have a middle or first name of Eucharii, which is possible since that is similar to his fathers name (Eucharius).  With a typical timing from birth to marriage of roughly 20 years this would fit. Here is a FamilySearch decendancy view of the Eucharius Koberstein line.

Here is a clip of the original record:

Items 1 - 2, Items 4 - 5: Kirchenbuch, 1592-1808
Author: Evangelische Kirche. Barfüßer Klosterkirche Heidelberg
BARFÜSSER KLOSTERKIRCHE: Heiraten 1593-1623, 1650-1657, 1657-1659, 1633-1692 --
Kommunikanten 1656-1682 -- Tote 1633-1634, 1650-1692 -- Kommunikanten 1682-1692 -- Heiraten 1709-1803
Family History Library International Film 1189252 Items 4 - 5 DGS Film # 102078163 Image 592

record title: Germany Births and Baptisms, 1558-1898 
name: Georgius Coberstein 
gender: Male 
baptism/christening date: 03 May 1607 
baptism/christening place: Barfüßer Klosterkirche, Heidelberg, Baden, Germany 
father's name: Michael Coberstein 
mother's name: Susanna 
indexing project (batch) number: C93414-1 
system origin: Germany-EASy 
source film number: 1189251 

Here is a clip of the original record:
Kirchenbuch, 1592-1808
Film 1189251 item 7, DGS 102078162
Image 1059 of 1064



record title: Germany Births and Baptisms, 1558-1898 
name: Anna Coberstein 
gender: Female 
baptism/christening date: 03 Jul 1608 
baptism/christening place: Heidelberg, Baden, Germany 
father's name: Michael Coberstein 
mother's name: Susanna 
indexing project (batch) number: C93414-2 
system origin: Germany-EASy 
source film number: 1189252

Here is a clip of the original record.



Both Georgius and Anna could be children of Michael Koberstein in the "euchariu" Koberstein line.  However he would have to be a very young father.