The State of New York Mortgage Agency (SONYMA) was created in 1970. The nickname “Sonny Mae” has been cited in print since at least August 1981 and “Sony Mae” since at least October 1983. “Sonny Mae/Sony Mae” has not been trademarked and is not officially used by the agency.
   
Similar nicknames include “Fannie Mae” (Federal National Mortgage Association), “Freddie Mac” (Federal Home Loan Mortgage Corporation), “Ginnie Mae” (Government National Mortgage Association), “Sallie Mae” (Student Loan Marketing Association) and “Farmer Mac” (Federal Agricultural Mortgage Corporation).
   
 
Wikipedia: State of New York Mortgage Agency
The State of New York Mortgage Agency (SONYMA) is a public authority created in 1970 by the state government of New York to provide affordable homeownership to low- and moderate-income New Yorkers. It offers affordably priced fixed-rate mortgages through several mortgage programs for eligible homebuyers. Each program offers competitive interest rates, low down payments, down payment assistance and no prepayment penalties. SONYMA offers its programs through a network of participating lenders throughout New York state who contract with the agency to offer SONYMA’s programs to their customers. The mortgage loans are purchased from the lenders by SONYMA, which funds the purchases by issuing tax-exempt bonds.
 
SONYMA also runs a Mortgage Insurance Fund (MIF) to provide insurance for mortgages made by commercial and public lenders to finance construction of affordable multifamily apartment developments. The MIF also provides mortgage pool and primary insurance for single-family mortgages purchased by SONYMA. The MIF is funded from a surtax on the recording of mortgages in New York State.
     
New York (NY) Times
Sonny Mae Sets Bond Sale
Published: August 12, 1981
The State of New York Mortgage Agency, known as Sonny Mae, announced plans yesterday to sell $100 million to $125 million of single-family home mortgage revenue bonds.
   
New York (NY) Times
A Little Lift, at Least, for Housing
Published: June 26, 1982
(...)
First, the Legislature should broaden the powers of the State of New York Mortgage Agency. Sonny Mae, as it is called, was established to borrow money from the public at relatively low, tax-exempt rates of interest. It passes the money along to savings banks and other mortgage lenders, enabling them to reduce mortgage rates to homeowners and builders.
 
New York (NY) Times
PERSPECTIVES: LOAN PROGRAMS; LOW-COST MORTGAGES GO QUICKLY
By ALAN S. OSER
Published: October 30, 1983
LUCKILY for Robert Stern and his wife, Cheryl, they already had a contract to buy a house when loans became available last July through the sale of mortgage-revenue bonds by the State of New York Mortgage Agency.
(...)
From 3,700 to 4,000 families will benefit from lower-cost loans as a result of the new issue, said Wallace L. Ford 2d, executive director of the mortgage agency, known as Sony Mae.
 
Google Books
December 1983, Black Enterprise, pg. 84, col. 1:
SONYMA (popularly known as Sony Mae), was created by the New York State legislature in 1970 to provide banks with new sources of mortgage money for single family housing through the sale of tax-exempt bonds.
       
Google Books
Marshall Loeb’s 1986 Money Guide
By Marshall Loeb
Boston, MA: Little, Brown and Co.
1985
Pg. 112:
Sonny Mae stands for the State of New York Mortgage Agency, which issues bonds that are backed by fixed-rate mortgages.
 
New York (NY) Times
Sonny Mae Acts to Shorten Lines
Published: March 17, 1985
AT the State of New York Mortgage Agency, the policy of ‘‘first come, first served,’’ has seen its last.
(...)
Last year, according to figures from the agency (known as Sonny Mae after its acronym, SONYMA), the average income of home buyers who qualified for an agency-sponsored loan was $38,000 a year in the lower counties of New York State, $28,000 upstate.
 
New York (NY) Times
11 December 1986
FINANCE/NEW ISSUES; Sony Mae Plan Allows Mortgage Flexibility
The State of New York Mortgage Agency is offering $372 million of bonds in the second part of a financing that will give it more flexibility in setting interest rates on the low-cost mortgage loans it makes available to home buyers in the state. Using a new disbursement procedure, the agency will make low-cost mortgage money available gradually rather than all at once. Officials of Sony Mae, as the agency is known, hope to avoid a problem of past years when much of the money it had available was not used because declining interest rates made its mortgage rate unattractive. Last month the agency sold $333 million of bonds similar to this issue.
 
New York (NY) Times
Sony Mae Issue Of $90 Million
Published: March 29, 1989
The State of New York Mortgage Agency, which provides low-interest-rate financing for first-time home buyers, priced a $90 million reoffering of mortgage revenue bonds yesterday through underwriters led by Bear, Stearns & Company.
 
Google Books
New York Real Estate for Brokers
By Marcia Darvin Spada
Mason, OH: Cengage Learning
2009
Pg. 113:
The State of New York Mortgage Agency (SONYMA), also known as Sonny Mae, raises money from the sale of New York tax-free bonds, which is then used for mortgage loans.