Yes, It's possible but, you must have Shopify Plus account to do it.
There is Shopify app called "Script Editor" https://apps.shopify.com/script-editor which allow to reorder payment method listing on checkout. This app is only available to Shopify Plus customers.
Let me know if you have Shopify Plus account and need any help.
Found a solution! Won't work for every scenario, but if there's only like one or two you want to push to the top, what I did was simply add a space to the title of the manual payment method when you are creating it.
I only have 3 manual payment methods so it was easier for me to implement. Just deleted the middle one I wanted bumped to the top (since you can't edit the name/title of it) and recreated it, but this time with a space in front and voila, it now appears on top even though it starts with a C, and the next option starts with an A (I think the default is alphabetical order).
Hope this helps someone out there! I don't normally log in to leave comments like this, but this issue was really bothering me and I'm sure other sellers out there are effected by it as well.