If convenientlly possible ...

There is no concept of "if conveniently possible" in Japan, is there?

I have been told this is rude to say: 暇ならこの仕事やってください

If I try to suggest something as a "someday" kind of thing to my in-laws, they think I want it right away.

How can I say, "If you have time, then please do XYZ; otherwise, don't worry about it?"

THere are many ways to phrase it, but if it's your in-laws, you ask and probably they'd do it right away anyway :)

暇なら can sound like "if you've got nothing better to do (now)," and
この仕事やってください "please do this" is too blunt :)

If you want to phrase the above a bit more polite:
お時間があるときに、[ ]してもらえたら、助かります。
お手すきなときに、[ ]してもらえると　助かります。
(I would appreciate if it you could do [ ] if you happen to have some time.)

There are difference in the culture & attitude. Japanese tends to take seriously & put priority when asked to do something by others and complete right away. Otherwise they will tell you when they can do it or ask by when it must be done. So if you ask if convenient time, they will re-priotize to do your job before theirs. Some of the reasons are that they don't want to be asked again if they've done or not or they want to do it before they forget in their busy life or others think tardy.
I wish I had subordinates like them in US.(though there are other things to watch out using Japanese workers but I digrest).

"暇ならこの仕事やってください"

Is this in an office setting, or is this phrasing for your in-laws?

Either way, your phrasing can kind of come across as "Since you obviously have nothing more productive to do with your time, do this job/task." If this specific request is to your in-laws, "仕事" is almost never going to be the right choice of word if you are requesting that they do something for you.

"hima" is a tricky word. In certain contexts, it can be almost accusatory. Japanese tend to prize being diligent and hard working, so the idea of being thought to be in a state of not having anything productive to do can be insulting. (Obviously I am painting with a broad brush here. Of course there are lazy Japanese who don't care about being himajin, and there are also plenty of times where "hima' does not have insulting connotations.)

If you have a good relationship with your in-laws, and you ask for their help, even if it is not urgent or critical and you really don't require it to be done, they will want to help you and (depending on their character, of course) go out of their way to do what you ask. Since you are asking, you must need their help, right?That's what they will think, anyways.

You might try something along the lines of "お父さんの都合がよければ " or "お父さんの都合がいいとき " but you will want to run that past a native speaker to make sure it is OK.