The solution I'm offering doesn't limit to a specific date but rather to a specific range. It also allows travel beyond that limit, which will be either extremely inconvenient or unsafe, or likely both. This was inspired by real life, turns out whether you should use float, double or decimal sometimes matter a whole lot.
Time is much like space: better explored when you know where you're going. Anybody who've seen Stargate knows you need two things to travel: the coordinates of the destination, and the coordinates of the point of origin. Well, consider it's called space-time continuum for a reason, any point in time is therefore identified by coordinates. To find your way between now and then, you need to calculate a trajectory through time. Double the fun if time travel implies defining the location in time and space.
The basic conundrum is you can either do things fast or precise. You can travel between any two points with tip-top accuracy by using arbitrary-precision arithmetics (aka as infinite-precision, which sounds way cooler), a supercomputer and three years of your time. Note that you'll have to predict how long the calculation takes, and input the precise time of your departure in advance and stick to it with rigorous precision. If the calculation fails (computer crash or other calamity), you'll have lost all that time for nothing.
And then you'll have to do it again to calculate your way back in advance, since it's unlikely you'll find a supercomputer in the 1940s. If anything goes wrong, if you meet an unexpected obstacle, and if you miss your mark going back or forth, there is zero guarantee you'll be anywhere near where/when you want.
All in all, you can dismiss that possibility by denying access to the appropriate resources, supercomputer time ain't cheap, nor is the power plant to get the lights on, or by making your characters sane enough to not consider doing it that way.
So instead you'll aim for something fast using built-in floating-point arithmetics. It will take a couple of minutes at most but the trade off is accuracy. There is a range of time where you're 95% certain that you will be where and when you want, give or take a day or two. Beyond that, the machine might send you to the Moon and miss the date by a century.
Essentially, the further you go, the worst your odds are. As a good software dev, you've put blocks that limits use to a defined safe range. It just happens 1941 is the limit if you were to start travelling from today.
Obviously, that opens the door for someone to travel by increments. If you have a 10 year range and want to travel 100 years back, you'll just do it in 10 steps. Well, to close that door, the machine can have an autonomous power supply that is good for two travel and a half, one in, one back and some reserve for rainy days, and then you are stuck in time forever. Also allows you to sacrifice your time machine to do something really important.
You might also have an unsafe mode hidden and accessed by typing Ctrl+Shift+C and enter rosebud, but it's called unsafe for a reason. It might just transform you into a fly instead of doing what you ask. So again, you would not consider doing that unless you had really important and dramatic reasons for it.