per Grok ai: No, there doesn't appear to be a notable popular song exactly titled "A Cottage for Two" from the 1930s or 1940s.
However, there are some very similar titles and themes from around that era (or close to it) that might be what you're thinking of:
"A Cottage for Sale" (1929/1930) — This is a well-known standard composed by Willard Robison with lyrics by Larry Conley. It was recorded by artists like Ruth Etting (1930) and later Peggy Lee. It's a melancholic song about lost love and a home that's now for sale.
"While Others Are Building Castles in the Air (I'll Build a Cottage for Two)" (1919) — Written by Jack Mahoney (lyrics) and Fred Fisher (music). This was a popular song from the post-WWI era with recordings by John Steel, Henry Burr, and others. It was still being referenced or re-recorded into the 1940s. The theme is romantic and down-to-earth: preferring a simple life together over grand dreams.
There's also a modern track called "A Cottage for Two" by Geoffrey Peter Gascoyne & Anita Wardell (released in 2025 as part of a 50s-style jazz album), but that's obviously much later.
