This thread should be in Modding Questions/Help anyway, but it's alright.
The same question was already asked several times like
this,
this,
this,
this, and
this. Most mods in Bully use STimeCycle.lur for freeroam mods and ArcRace1.lur for custom mission mods, the .LUR files are compiled scripts stored within the .IMG archive if you don't aware of that before.
In simple term, you cannot have two mods replacing the same script. Your best chance are combining STimeCycle.lur and ArcRace1.lur via
IMG Tool 2.0 by extracting them and adding them to the other one.
OR.. you can use
More Scripts to Replace (MSR) to add up to 4 freeroam mods and 100 custom mission mods. I made that tool a couple years ago for people who don't know scripting on Bully, so you can just replace my scripts instead of your favorite STimeCycle.lur mod.
Just make sure you read the "README.txt" properly.