It is a slightly common question among roll hunters.
Here's an answer. You can't.
during the
State Quarters you could ask a bank to order you rolls and they would get what you wanted during the release period from the federal reserve.
This no longer happens and new coin has been outsourced to the armored carriers for distribution.
The bank (unless your particular bank has a tight connection with someone at the armored carrier for the change orders) gets what they get from the armored carrier and it is what it is, they don't get to pick or choose, they just get whatever is delivered, and sometimes it's new coin, sometimes is new coin from last year, or two years ago, sometimes it's circulated re-rolls from the coin collection machines.
Now there are ways to up your chances to get new coin. Ideally, you'd want to select a bank in a business district, a bank where it's likely their customers are businesses and need change orders filled, this will guarantee they get regular shipments of coin to meet demands and your changes go up as opposed to going to a bank in a residential area, where its likely people will deposit hand rolled change and they will dump it off on anyone that wants it and order much less from the armored carrier.
Another option is to talk to your bank about ordering you a box of the coin you wish to search. if it's quarters then you'd need $500 to buy it each week. as long as you don't search it and return it to them, They will likely continue, but if you stop you should let your bank connection know, so he's not ordering for you and getting stuck with it, even then, there will be times when the customers bring in a lot of change and their inventory won't allow them to place a order for that coin, in which case, it's best to take the re-rolls to run them down so they can place an order the next week.
Now if you do this box a week method, this is likely your best chance of finding new coin. eventually whole BU new boxes will turn up.
As far as getting rid of the coins you don't want, best to find a bank or credit union with a no fee machine to dump at and get an account.
if it is dollar coins or half dollar coins, this complicates things further, banks hate them because they aren't normally used in commerce. it will be hard to get those.
pennies, nickels, dimes, quarters are usually no problem. I search quarters and the observations I listed above worked out for me, but be prepared to not get new coin a whole lot, and happily surprised when the box is an entire BU box. it's hit or miss, but there isn't a way to get exactly what you want on order anymore.
if you can dump at zero cost, build a relationship with your bank, and get a weekly box, you can pickup on like a monday and search, and dump before the week ends, and have most of the $500 back for the next week box short the coins you wanted to keep and just keep rolling it over.
Now if you aren't hunting W quarters, and want new rolls of coins for having new rolls of coins, I'd say buy them online and just get a roll or two and no hunting around.
I've never had any luck with Ws from online sellers of BU rolls, but it's good for the P or D examples that we are usually harder to get depending on the side of the country you live on until a year or two later when they circulate some.
if you do buy from online sellers remember the face value of the coins and add some profit, but don't overpay for them there will be shipping too of course, so best to try to do it all in one shot if you can or look for free shipping offers.