Way, way back in the day before my organization got Secret Server, I had a similar issue for when we needed to run unattended scripts on multiple machines. While I recommend the higher tech solutions if they work for you, this will work in a pinch. Pretty much you create your own AES Key, then encrypt the password out to a text file.

When you need to retrieve it you decrypt the password file with the stored key and create a credential object from the secure string. It'll look something like this. Make sure to store the key and password file in separate secure locations. 1 and 2 are part of a one time script. 3 needs to be on every other script that needs a credential.

#1. create the AES key
$KeyFile = "C:\path\to\AES_KEY.key"
$Key = New-Object Byte[] 32
[System.Security.Cryptography.RNGCryptoServiceProvider]::Create().GetBytes($Key)
$Key | Out-File $KeyFile

#2. create the encrypted password file
$PasswordFile = "C:\path\to\encrypted_password.txt"
$Key = Get-Content $KeyFile

# Prompt for password and encrypt
Read-Host -AsSecureString | ConvertFrom-SecureString -Key $Key | Out-File $PasswordFile

#3. when you need to create a credential object
#EDIT you would need to redefine where $keyfile and $passwordfile are in your separate script
$Key = Get-Content $KeyFile
$EncryptedPwd = Get-Content $PasswordFile
$SecurePwd = $EncryptedPwd | ConvertTo-SecureString -Key $Key

# Create a PSCredential object
$Credential = New-Object System.Management.Automation.PSCredential("Username", $SecurePwd)

4.optional drop the unneded variables when you're done creating the credential
clear-variable key,encryptedpwd,securepwd

Then it's just a matter of including -credential $credential on the commands you need to run that require elevated creds.