You have an interesting problem.
Familysearch.org has the death of Don E. Meyka b. 25 Feb 1895 in Tyler Co., TX d. 13 Mar 1957 in Harris Co., TX. His parents are listed as Tom Meyka and Zula Reed. Don married a Viola Cain.
There is a Martha Zula Davis b. 2 Oct 1875 in Colmesnell, TX with father Thomas Washington Reed. In 1900 she is living with her father in Tyler Co., Tx. Interesting, since Don E. was born in 1895 and Bonita was born in 1902 (according to the 1910 census). Perhaps, Don was raised by relatives
I think that Don E. is likely a brother of Bonita and Tommie. The name doesn't seem to be very common in Tyler Co.
That being said, as Tom Mezka was German, It is possible that Mezka is a slaughtered version of the name Metzger (this is the German word for butcher). The German pronunciation of the name could easily be understand as "Metzka". However, there are always other possibilities, but it is something to keep in mind.
I could not find any marriages for Zula, whether for Tom Meyka or Richard Davis. Interestingly enough, I cannot find Don E. in the 1900-1920 census, despite the fact that he filled out a draft card for WWI in Tyler Co. I first find him in the 1930 census with his wife and family.
I did find that other Meyka researchers discussed Tom and Zula back in 2009. Try this link:http://boards.ancestry.com/thread.aspx?mv=flat&m=1074&am...
Otherwise, do a search on Google for "Don Enloe Meyka" and it should pop up.
Hopefully, this is some help.