A letter is the most reliable channel for this. Write a short note with your phone number clearly at the top and send it through InmateAid or regular mail. It arrives physically, it does not get filtered or lost in a system queue, and once they have it they have your number to reference every time they want to call. If your emails are going through the CorrLinks system, keep in mind there is a delay built in for screening, and not every facility has email available.
If you need to reach them faster than a letter allows, your best option is to get word through someone who already has regular phone contact with them. A family member or mutual contact who is on their approved call list can pass along the message in their next conversation.
Asking staff to relay a message is technically against the rules at most facilities, though in practice some staff members will help with something as simple as a phone number. Whether that works depends entirely on who picks up and how they feel about it that day. It is not a strategy to count on.
The letter is always the most dependable path. Send it now and the number will be in their hands within a week.