Tough question, but I think I can give you an estimate based on BMI's licensing system. You can check out their complete licensing form for venues (including theaters) that contain fewer than 10,000 seats (I assume this is the case for the theater you're talking about!) at http://www.bmi.com/licensing/forms/facilitiesmore.pdf.

First off, royalty rates are determined by a very complicated formula that takes in the type of performance, number of seats, gate gross, and a bunch of other stuff, depending on the licensing organization (ASCAP, BMI, or SESAC). However, BMI does provide some flat-rate info for charity performances, so we'll take it from there. IF you were a member of BMI, and IF the proceeds were to be donated to charity (if the theater is non-profit, we'll make that argument, mostly because I can't find any other fee schedules), what would happen would be the theater would apply for a license to peform the songs. BMI would then charge them at the following rate:

Seating capacity of 0-250: $15 per performance
Seating capacity of 251-750: $18 per performance
Seating capacity of 751-15000: $28 per performance

There's more for larger theaters, but you can check those out at the above-mentioned URL if you need to. Now, the SONGWRITER would receive a percentage of those royalties, anybody else who needs to be paid (producer, performer, etc.) would get a percentage, and BMI would take the rest. Since you're not going through BMI, a fair charge would probably be 25-50% of these rates. So for a 7-show run in a 200-seat theater at 40% of BMI's rates, you could ask for $42. To my mind, even this would probably be a bit excessive, UNLESS you sold the songs to them outright and let them keep them for all future use, mostly because you're not a member of BMI and haven't had the expense of their annual membership fee (I think that's about $150/yr, but don't quote me on that).

On the other hand, for custom composition for one-time use, you could possibly charge more. If the theater balks at paying more (after all, they could probably pay about $150 and cover royalties for most or all of the songs they play in their theater for an entire year), you could donate the songs to the theater, set a higher rate of compensation at what you think they're worth, and ask the theater to write you a receipt for a donation that you could then use for tax purposes.

If you plan on using these songs in other venues, you might want to look into BMI, ASCAP or SESAC membership. Just add ".com" to the names and you have the URLs. Hope this helps!