Your question divides into two parts: How to change a MAC address, and how to time a certain process.
Change MAC address
Given you cannot install nice utilities like macchanger, you will have to do this manually.
Find out your network interface name. In many cases this is eth0. Be sure to find the name of the interface you really want to change (WAN or LAN, VLAN...). In this example, I'll use eth0
Check your current MAC address ip link show eth0. It may show something like link/ether 00:11:22:33:44:55
Take down your interface: ip link set dev eth0 down. This is a large disadvantage of this solution because it tears down the whole network during the process. Be sure you really want this to happen.
Set a new MAC address: ip link set dev eth0 address AA:BB:CC:DD:EE:FF
Take your interface up again: ip link set dev eth0 up
Make a script of it
In a script, this might look like this:
#!/bin/bash
IF=eth0
# Create a Random MAC, inspired by http://superuser.com/a/218372/475723
# MAC might not be valid since it's completely random. Use the linked answer to add a prefix like 00:60:2F
hexchars="0123456789ABCDEF"
MAC=$(for i in {1..12} ; do echo -n ${hexchars:$(( $RANDOM % 16 )):1} ; done | sed -e 's/\(..\)/\1:/g;s/:$//')
ip link set dev $IF down
ip link set dev $IF address $MAC
ip link set dev $IF up
Save this script to a fitting location (let's assume /root/mac.sh) and make it executable by chmod +x /root/mac.sh.
You can test your script by executing /root/mac.sh.
Time running processes by cron
With cron you can make processes run on a regular basis, for example once a day.
Edit your cron file by crontab -e
Insert a line giving the necessary information: When and what. For example 0 1 * * * /root/mac.sh. This would execute the command every day, month, year at 01:00. Please check the cron help pages for information on how to set it to different intervals.
Please be sure to edit the crontab file as root.