I think you should parse it this way:
The けど continues to 明日頑張ろう "I'll do my best on the next day", not to 思い通りにならない日は "on the day when things don't go well / if things don't go well on a day".
So the lyrics literally mean:
時には雨も降って - At times, rain would fall and
涙も溢れるけど - tears would overflow, ...
Just about your question about けど in comments; “but” isn’t the only meaning for it; I suggest you read this https://bit.ly/2T36LD8 I’m not good at explaining but basically けど and が can also work as ways to naturally build up on the prior sentence and continue based on it. that means they can sometimes be translated as “and” or “so” in english.
～つ can refer to one's age. See: In 星の王子さま, what is this 六つのとき?
So it's "The love with you who is as many as 9 years apart in age". 君 can be either younger or older. (Judging from the whole lyrics, I feel 君 is 9 years younger because she seems to be better at SNS, but you cannot tell this from the title alone.)