〔地球温暖化の原因とされる〕メタンガス
As the other poster says, 地球温暖化の原因とされる is a relative clause that modifies メタンガス.
Now how about thinking of it this way...
Its non-relative version is: メタンガスが地球温暖化の原因とされる
「XXがYYとされる」 -- "XX is regarded as YY" "XX is considered to be YY".
So this literally means "Methane is regarded as the source of global warming".
And its non-passive version can be: (我々が)メタンを地球温暖化の原因とする
「(人が)XXをYYとする」 -- "(Someone) regard XX as YY".
which literally means "(We) regard methane as the source of global warming".
So the phrase in your sentence literally means:
"Methane, which is regarded as the source of global warming"
For this grammar point, @Naruto's answer in this thread might help:
Did I parse and interprete this sentence correctly?
How about parsing the sentence this way:
〔〈(地球温暖化の原因とされる)メタンガスをあまり出さない〉牛をどうしたら作ることができるか*〕も提案できる
Lit. "We/I will be able to propose 〔how we/they can make cows 〈which don't emit much methane (which is considered as the source of global warming)〉〕.
*「どうしたら/どうすれば~~できるか」「どうしたら/どうすれば + potential」 means "How we can do~~" "What we should do to~~".