Find out what chains in your areas currently have some type of entertainment, and approach them specifically. Also, again assuming you are at least partly a children's entertainer, find out which ones have a Kids' Night (usually with a special menu and prices, and usually Tuesday nights in these parts). Sunday brunches are good, too.
Don't know what chains you have, but TGIFriday's, Green Hills Grille, Olive Garden, Outback's, Red Lobster, and Tia's Tex-Mex have all hired or are currently employing magicians around here.
For these such restaurants, a success rate of one in forty sounds low to me. I'd put it at one in five or ten. But it probably all depends on your sales pitch, demo, and price.
IF you will be performing at a family restaurant and directing most of your table-side performances to kids, be sure to include that benefit when you have your brief prearranged appointment with the GM.
Assuming that you are already a somewhat entertaining close-up guy, and are able to deliver the following goods, say that you will make sure the kids laugh and have fun when you visit their table, and that you make balloon animals, too. (More about that if interested.) Tell the manager that the KIDS will bring the PARENTS back to the restaurant. (They will.) Tell the manager that one of your jobs as a Table-side Entertainer (I never cared for the fancy snow-job title "in-house promotions coordinator", or whatever.) is to make sure that current regular guests (customers) at the restaurant return to it even MORE often than they already do.
Perhaps now more than ever, pricing is important. Mention your usual private-party rate before mentioning your restaurant rate. And don't mention prices until the manager asks. Try to get across all your other benefits, and even get through your free demo hours, before having to mention the benefit of him/her hiring such a fun entertainer at such a reasonable price.
In fact, at your brief meeting with the GM try just to introduce yourself, give him/her a business card, mention your benefits (you don't need to use the word), set up your demo time and day, and try hard to leave and let them get back to work.
IF your primary goal is to get a regular paying gig at some price (but not at just any price), and if they say your price for a three hour shift is too high, consider offering them a two hour shift for the first six weeks until their new entertainment program catches on.
Ideally, you get a regular gig at a busy busy place that loves for you to keep the guests happy while they're waiting forty-five minutes in the lobby or bar to be seated.
Realistically, in these perhaps tougher times, here's something you might consider: tell the manager your fee for a two or three-hour evening of restaurant entertainment. Tell him/her that you will adjust that price in his/her favor on nights when there are slow spells, before word gets out that you're entertaining there on a regular basis. Say that you will just informally clock out (and have a snack or read or practice) for a while until business picks up again that night, and you will charge the restaurant accordingly for that night. You might also mention that, if you're available, on nights when the crowd is still coming in at the end of your shift you will work extra time for extra pay IF the manager okays it at that time. Upside? You may get a regular gig that you'd otherwise lose. Downside? Some nights you'll make less money (excluding tips) than others.
Many restaurant gigs do not themselves pay (all) the bills. But of course they provide other benefits.