As others have pointed out by now there is no automatic right of a child born in Thailand to foriegn (not Thai citizens) parents.
A child born to non-Thai parents is assumed to be of whatever nationality his/her parents are.
Now if ONE of the parents is in fact a Thai citizen...that's a different story. In that case the parents could register the child as Thai based on the citizenship of the Thai parent.
Many years ago the father had to be Thai citizen..but the law was changed quite a few years back and now if either of the parents is Thai, the child can be legally Thai also.
But for a child born in Thailand of two non-Thai parents...I don't believe Thai citizenship or even Thai residency is possible for the child. (Except as an adult by going through the whole Thai Permanent Resident process).
I believe, but I could be wrong however, that for visa purposes a minor child (not old enough to legally handle their own visa application for example) will be allowed to stay in Thailand based on their parents visa status until the child is old enough to legally handle his/her own visa status (i.e. they have attained the legal age to sign the documents required).
If you want to register your child as a citizen of your country...and legally attest to that fact...your country's embessy will know how to take care of that. They will probably require proof of the child's birth in Thailand from the hospital and proof/ certfication that both parents are citizens of your country.
But that's a different matter.