For the citations, it's possible to define a new option for cases where you know there is no author:
% Define a new type of APA citation for title
\definebtx[apa:cite:noauthor][apa:cite:authoryear]
\startsetups btx:apa:cite:noauthor
\btxcitereference
\quotation{\btxflush{title}}
\btxcomma
\btxflush{year}
\stopsetups
So instead of \cite[noname2012], you would use \cite[noauthor][noname2012]. This solution is based on the example on page 52 of the publications manual.
As for the bibliography, you'd probably have to overwrite the basic article definition. For the following, I copy and pasted the standard definition from the source and added a switch to test if there is no author:
% Define a switch in bibliography entry
\startsetups btx:apa:list:article
\doiftextelse{\btxdirect{author}} {
\texdefinition{btx:apa:authoryear}
\texdefinition{btx:apa:title-if-not-placed}
} {
%If no author, use title as first entry
\btxflush{title}
\btxperiod
\btxleftparenthesis
\btxflush{year}
\btxrightparenthesis
\btxperiod
}
\btxdoif {type} {
\btxleftbracket
\btxflush{type}
\btxrightbracketperiod
}
\texdefinition{btx:apa:journal-volume-number-pages}
\texdefinition{btx:apa:url-doi-note}
\stopsetups
If needed, a similar switch could be used in the citation to automatically handle the author/noauthor cases.
Combined together with demonstration:
\startbuffer[ref]
@article{solo,
author = {Lastname, Firstname},
title = {Title with author},
journal = {Journal},
year = {2000},
month = {1},
volume = {1}
}
@article{none,
author = {},
title = {Title with no author},
journal = {Journal},
month = {1},
year = {2000},
volume = {1}
}
\stopbuffer
% Boilerplate to set up references
\loadbtxdefinitionfile[apa]
\usebtxdataset[ref][ref.buffer]
\setupbtx[dataset=ref]
\definebtxrendering[ref]
[dataset=ref,
specification=apa]
\setupbtx[apa:cite]
[alternative=authoryear,
etallimit=1]
% Define a new type of APA citation for title
\definebtx[apa:cite:noauthor][apa:cite:authoryear]
\startsetups btx:apa:cite:noauthor
\btxcitereference
\quotation{\btxflush{title}}
\btxcomma
\btxflush{year}
\stopsetups
% Define a switch in bibliography entry
\startsetups btx:apa:list:article
\doiftextelse{\btxdirect{author}} {
\texdefinition{btx:apa:authoryear}
\texdefinition{btx:apa:title-if-not-placed}
} {
%If no author, use title as first entry
\btxflush{title}
\btxperiod
\btxleftparenthesis
\btxflush{year}
\btxrightparenthesis
\btxperiod
}
\btxdoif {type} {
\btxleftbracket
\btxflush{type}
\btxrightbracketperiod
}
\texdefinition{btx:apa:journal-volume-number-pages}
\texdefinition{btx:apa:url-doi-note}
\stopsetups
% Testing
\starttext
Normal citations: \cite[solo] vs. \cite[none] \\
Noauthor citations: \cite[noauthor][solo] vs. \cite[noauthor][none]
\startsubject[title=Bibliography]
\placelistofpublications[ref][method=dataset]
\stopsection
\stoptext
With the result:

However, as Mico suggested in the comments, it's easier to simply make the organization an author:
\startbuffer[ref]
@article{solo,
author = {Lastname, Firstname},
title = {Title with author},
journal = {Journal},
year = {2000},
month = {1},
volume = {1}
}
@article{none,
author = {{Professional organization XYZ}},
title = {Title with no author},
journal = {Journal},
month = {1},
year = {2000},
volume = {1}
}
\stopbuffer
% Boilerplate to set up references
\loadbtxdefinitionfile[apa]
\usebtxdataset[ref][ref.buffer]
\setupbtx[dataset=ref]
\definebtxrendering[ref]
[dataset=ref,
specification=apa]
\setupbtx[apa:cite]
[alternative=authoryear,
etallimit=1]
% Testing
\starttext
Normal citations: \cite[solo] vs. \cite[none] \\
\startsubject[title=Bibliography]
\placelistofpublications[ref][method=dataset]
\stopsection
\stoptext
With the result:

author = "{Securities and Exchange Commission}". – Mico Mar 16 '13 at 23:43