Well, ask yourself one question, can you do something else? Then do that. The only reason to be an actor is because you HAVE to be an actor. It is a compulsion, a sickness of sorts. Try giving it up, if you can, then it wasn't meant to be.

I was once told, "if you are ten minutes early, then you are on time, if you show up on time, you are ten minutes late." Give yourself some time prior to rehearsal to clear your head and prepare yourself to be productive. Ask if you are supposed to come warmed up physically and vocally. If so, start in your car on the way there. Remember, the better your practice the better you will perform.

Don't be silly.

Professionalism is key. Ideally, one would never have to handle this sort of juggling. You'll put your best foot forward if you respect what flexibility your current production can offer. Let the 2nd production know those limitations, and if they really want to consider you they will find a way. Be honest about your hopes with both groups, and - wanting a positive team member - they will try to accommodate if they can. Producers don't want to learn that your focus can be split in production, they want 100% of your talent for the project at hand. If show #2 doesn't work out, take a deep breath & let it go. There is ALWAYS another perfect production that fate has ready for you.

Here are seven steps:
[1] FINDING.
Read scripts, first person books or stories, monolog collections. Find pieces that interest you. Find characters with which you find a connection. Note ANYTHING that might work - you'll need more than one monolog in your repertoire.
[2] CUTTING.
When learning your new pieces, try several versions - differing in length, cuts and focus. Without rushing, find pieces that can fit 1 minute, 2 minutes, 3 minutes or a variety!
[3] MEMORIZATION.
Contrary to popular fears, getting your lines down should NOT be the biggest hurdle in your acting career. You have to do it, so get it done. Hit and miss for a few rehearsals of your monolog, but get rid of the script as soon as possible - sooner!
[4] CONNECTION.
You must connect with each and every moment of your monolog - down to the pauses between words & the "a's, an's and the's!" Understand what lies beneath and keep learning. Try 'dropping in,' visualization and physicalization to get there.
[5] PHYSICALITY.
Support your words with what you do. Scripts do not have to be based in words, but in what is unspoken yet communicated. Think about posture, gesture, movement, expressions, and interaction with other people and objects. Now forget that. Be there 100%.
[6] REHEARSAL.
Your monolog is your touring solo performance, so put effort into it. If you are struggling to remember lines, don't expect your best acting to come through. Go through your top monologs every week - and perform them for your friend or instructor on a regular basis. Pull out the less used ones every once in a while & dust them off out loud.
[7] PERFORMANCE.
Get out and USE your monologs! Audition, audition, audition. Have enough of a repertoire that you can tailor your audition to specific shows & roles. Assess your monolog performance honestly. Realize which monologs suit you best for your different attitudes.

Go get 'em!

First off, you will find that at all different ages there are times when it feels like no productions are calling for actors of your age, shape, sex and abilities. Keep looking - there are shows out there for all! At age 24, there are actually many roles that would fit you. If you look younger, know that you will have the opportunity to bring you actual-age maturity to younger roles in a way no younger person could, so don't avoid them. There are great leading roles of all ages out there. Think about the companies for which you audition: talk to the companies [or casting agents] for which you'd like to work, and ask directly what roles they are offering for someone of your age who can play younger. You are smart to be realistic about the type of monologs to use. Find roles from age 15 - 30 [or older, if the age is not really important to the character] which [a] interest you, [b] seem like your real-life personality, or [c] are from well-known scripts. You do not mention whether you are a man or a woman, which would give me a good starting point. Look at the cast lists and start reading! Many script publishing companies list that information online, and then you can find the scripts at a local library.