Hello,
I have a couple of street maps of Budapest from the 1950's and 1960's but none of the XIX District unfortunately. I do however have a book entitled "Budapest tmutat" from 1957. It lists all the streets of Budapest, what bus to catch to get there and what their new name is, if applicable. If there is a particular street you are interested in , perhaps that this book might give you some information.
You may also want to check out
http://budapest19ker.lap.hu/ which seems to have a number of links that may help you track down any information:
e.g.
http://www.museum.hu/search/museum.asp?ID=38 or
http://www.kispest.hu/news.php?group=29When I lived in the IV District a number of years ago I came across part of the local government site that a history of street names for that part of Budapest. Very interesting indeed.