What to charge, what to do

I have been approached by a business that does a lot of parties at their venue. It is an indoor mini golf and arcade. I left my card there last month when I took my family to play, and had painted everyone up. The staff loved it and asked for my info.

Anyways, they are interested in hiring me to come in once a week and paint, on Saturdays, which is their busiest day and has back to back parties.
I did let them know that Saturdays are busy party days for me as well, but perhaps we can work it out where I paint during my not so busy times.

My initial thought is to give a multi hour discount. Say, if they hire me for 6 hours per month it is $$ rate, for more than six it is $ rate.

Any thoughts? I have to work up a proposal and bring in some design pictures tomorrow.
I was also thinking to propose adding me to party packages, where they can add a percentage on top so we both make money.

Is this company offering your services for a free add-on to a party they're already hosting? I doubt it. I bet they tack on an extra couple of bucks for the extra service. You should know how much they are making off you and go from there.

They want to offer me to anyone there to play, so parties and individuals who are just there for a game of golf.

I would not want to be locked into a discounted weekend gig. If I did give a discount it sure wouldn't be much, maybe 10% on a longer booking. What I would try to push in your proposal is the benefits of a weekday gig- If the arcade is already busy on Saturdays then wouldn't they want to encourage people to come in on other days as well. "Oh look! They're having a facepainter here on Tuesday. We should come in then" You can give a bigger discount for the weekday. Even Friday or Sunday afternoon- Are less prime than Saturday.

I would probably offer them 15-20% off of my hourly rates and ask them for a regular and consistent time. This is an opportunity to develop regular clientelle at the venue... a following. Depending on their hours of operation, you could set it to be in the early afternoon so that it wouldn't interfere with parties that much. In the summer time, I usually have a market gig every Saturday, but I'm done by 2pm and can still make pretty much any party that calls me. You want to develop regulars that follow you around, it really helps your ppf events. It is also a great opportunity to spread the word because you can brand yourself heavily while you are there. Yes, exposure can kill you, but this is a chance to get paid AND get exposure.