I can’t get away from the name [name_f]Molly[/name_f]. I just absolutely love everything about it and would love to name a future daughter this name. However, I have a nephew who I am very, very close to (and envisage our children being very close too) called [name_u]Ollie[/name_u] ([name_m]Oliver[/name_m].) So my parents would have grandchildren named [name_u]Ollie[/name_u] and [name_f]Molly[/name_f].
Too much/keep looking?
I’m super close to my nieces and nephews. But I didn’t take their names into consideration at all when choosing my kid’s names. Of course I wouldn’t use the same name but similarities are fine. And especially since [name_u]Ollie[/name_u] is actually [name_m]Oliver[/name_m], I definitely wouldn’t let his name stop you from using the girl name you really love.
I adore [name_f]Molly[/name_f].
I agree with PP that [name_f]Molly[/name_f] and [name_u]Ollie[/name_u] are fine for cousins, and that as long as you don’t use the same exact name it’s fine. I actually know someone who has stuffed animals named [name_f]Molly[/name_f] and [name_u]Ollie[/name_u], and they don’t get confused 
If it really bothers you, you could call her by her first and middle name around the family. Or a variation of it if it’s too long, like [name_f]Molly[/name_f] [name_u]Jo[/name_u] if her first and middle name is [name_f]Molly[/name_f] [name_f]Josephine[/name_f].
My brother is [name_u]Danny[/name_u], and I have a cousin named [name_f]Annie[/name_f] (to be fair he is about seven years older, and we don’t live close together anymore, but we did at one point) and I’m [name_f]Amy[/name_f], and when we lived closer to my cousins we were six months apart and named [name_f]Amy[/name_f] and [name_f]Annie[/name_f]. Not rhyming, but pretty similar. Never bothered anyone.
I think it’s only a problem if it’s the exact same name.
Honestly, I think it’s absolutely fine! I agree with one of the previous posters that it’s only an issue if it’s the same name.
I have a cousin ([name_m]Pate[/name_m]) whose name rhymes with mine ([name_f]Katherine[/name_f] called [name_f]Kate[/name_f]) and it isn’t confusing. I loved the special connection growing up.
I also think it’s fine!
I think it’ll bring some extra humour and warmth to their relationship - it’s a nice thing! You could use [name_f]Mary[/name_f] nn [name_f]Molly[/name_f] if it helps you but I don’t think that’s necessary especially since his name is [name_m]Oliver[/name_m] and he’s not an older bro, for eg.
I think it’s fine too, especially as he is actually [name_m]Oliver[/name_m] and might go by that as he gets older. [name_f]Molly[/name_f] and [name_f]Holly[/name_f] would be harder to reconcile, I think, and even then it’s a cousin not a sibling. In my extended family, they often used the same names over and over again, so there are many Elizabeths, Peters, [name_m]Georges[/name_m], [name_f]Marys[/name_f], etc. And nobody seemed bothered by sharing the same name at all. So go for it.
I think it’s fine! Their names would be [name_f]Molly[/name_f] and [name_m]Oliver[/name_m], and the nicknames are spelled differently so that makes it less matchy in my mind, and they aren’t the same gender so that separates them even more. I bet loads of people wouldn’t even notice the similarities- and they’re both lovely names!
I agree with others - [name_f]Molly[/name_f] and [name_m]Oliver[/name_m] are fine as cousins, even if he is called [name_u]Ollie[/name_u] often.
My name rhymes with my cousins nickname. It was never an issue.