Space on the blockchain is essentially auctioned off. If you are willing to wait a day, the best you can do is wait until there is a block with little enough competition for you to run your transaction at your desired price. This is no cheaper then sending your transaction immidietly if you happen to do so when the price is cheep.
Bitcoin used to have a concept of "priority" transactions that would allow transactions to process regardless of fees if there inputs are old enough; however this is effectivly disabled in modern Bitcoin.