In this case, "try" and "try out" both mean "to test/examine".
You have to look at what comes after the "try":
- try + noun = test: Shall we try the new restaurant?
- try out + noun = test: I want to try out the new Mercedes.
- try out + for = attempt: I'm going to try out for the football team.
- try + on = test clothing/accessories: Try on this perfume and see if you like it.
- try + infinitive = attempt: Let's try to get seats close to the stage.
Check your question to see how I edited your example questions.
The cited use of certain is syntactically valid, but it's not really idiomatically acceptable. The well-established "standard" usage fore the context is Some weeks I'd like to do X.
But there's also a semantic issue involved. In contexts such as...
The review board recommended parole for some prisoners
The review board recommended parole for certain prisoners
...it's tempting to say the highlighted terms are interchangeable, but actually they're not exactly equivalent. When certain is used in this way, it doesn't just mean some - it always carries the implication some specific [weeks, prisoners, etc.], where (in principle, at least) there is some reasonably clear-cut way of identifying which particular weeks / prisoners fall into the relevant category (weeks when a drummer will be hired, prisoners who will be granted parole).
TL;DR: When certain replaces some, it always implies certain specific / particular. Which doesn't make much sense in OP's context, making the cited usage non-idiomatic to most native speakers.
The general principle (for many/most people, but clearly not all native speakers - as shown by certain/some1 answers and votes on this page) is that some is often used to refer to a "random" subset, whereas certain normally implies reference to a "pre-determined" subset (or one for which the relevant inclusion criteria are available, at least in principle).
1 Using certain in this exact context would strongly imply I know exactly which posts I'm referring to (and you could probably figure it out easily if you took the trouble). Any such implication is weaker or non-existent with some.
Best Answer
Normally, you simplest way of expressing this is to spell out the names of the months.
If this is April, then just say the following:
There is no way of misinterpreting that, and it's also the shortest sentence.
If you say in the last two months, then, yes, it could be misinterpreted as meaning March and April—not February and March.
It's possible you could say the following:
Since April isn't completed yet, it would likely be assumed not to include any part of April.
However, I would still not rely on everybody understanding that interpretation. And, even if they did, it sounds odd, because it's not normally expressed in that way.
But in the case of a prize, needing to have made a purchase, and being unable to give the names of the months, this might work:
However, I've been told in comments that some people don't find there to be any difference in meaning between previous and past in this sentence—and they would still assume it was talking about the last 61 days.
So, if you really want to make sure that the point is made, you can make it even more explicit:
Or, perhaps more simply: