-Yrgs Unlimited! I like it. It makes absolutely no sense, but I like it.
Ye Olde Monarchy Supply: Kings Unlimited
Indeterminate Objects: Things Unlimited
Jewelry: Rings Unlimited
Beekeeping: Stings Unlimited
Stick-on Decals: Clings Unlimited
Endless Trysts: Flings Unlimited
Giant ape paraphernalia: Kongs Unlimited
Assimilation needs: Borgs Unlimited
Animal compost: Dungs Unlimited,
Dent removal: Dings Unlimited,
Vietnamese currency: Dongs Unlimited,
Euphemism insertion service: Dangs Unlimited,
Impersonators of the Chinese president (kind of like an Elvis impersonator, but different): Dengs Unlimited,
Small auxiliary boats: Gigs Unilimited,
Telephone bells: Rings Unlimited,
Jokes: Gags Unlimited
That calls to mind an entirely different kind of store to me.
Probably just me, though.
14 K of Gs Unlimited.
(oops, too many syllables…)
The Straight Dope: Wags Unlimited
CVS and Rite-Aid et al would have to merge to become Drugs Unlimited.
A business which help enforce repayment of unofficial loans would be Thugs Unlimited.
A clothing shop might be Rags Unlimited (though who knows how well their stuff would sell!)
Simple - like “throatwarblermangrove” is pronounced “luxuryyacht”, “teemings” is pronounced “tings”.
Web-hosting service: Blogs Unlimited
Purveyor of spirits to the Royal Navy: Grogs Unlimited
Patient and implacable porters for carrying things through swamps: Slogs Unlimited,
Gastropods: Slugs Unlimited,
Insects: Bugs Unlimited,
Parameters for C programmers: Args Unlimited,
Casual clothing: Togs Unlimited,
Crow-based roadkill removal: Tugs Unlimited,
Rrally big trucks: Rigs Unlimited,
used clothing: Rags Unlimited,
Carpets: Rugs Unlimited,
Administrative bureaucracy: Regs Unlimited,
Titanium Inert Gas welding: TIGs unlimited…
It’s amazing how many of these there actually are.
sack based items Bags unlimited
high end french watches TAGs unlimited
slow watches Lags unlimited
OBGYN vags unlimited 
machine tools Jigs unlimted
Beer Store Kegs unlimited
hosiery Legs unlimited
Frog hunting Gigs unlimited
wheel nuts Lugs unlimited
coffee drinking vessels Mugs unlimited
Someone make me stop this is too fun 
Cross-dressing costumes: Drags Unlimited
Trendy Italian restaurant: Spags Unlimited
Product placement agency: Plugs Unlimited
Amazon.com: Everything’s Unlimited
Whoopsy! Totally missed the one syllable rule. So sorry if I ruined your day, sundog66.
As my mea culpa, please accept this:
Tropical Fish Store: Tangs Unlimited
Pet Shop: Fangs Unlimited
Antique Vase Shop: Mings Unlimited
Water Dowsing Services: Springs Unlimited
Cherry Tree Nursery: Bings Unlimited
You know what would make this more fun? Name business’s slogan, not the type of business:
“The Best Male Bordello in Northern Nevada”: Dongs Unlimited
The double whammy:
“World’s Largest BBQ and Shish Kabob Supply Wholesaler”: Tongs and Prongs Unlimited
And my big triple play finish:
“Asian Temporary Laborers, Construction Workers, and Drivers”: Wongs, Hongs and Fongs Unlimited
ty, ty I’ll be here all week.
Dogs That Can’t Breathe Right: Pugs Unlimited
Please don’t kill me dog lovers!
A store staffed entirely by Frenchmen: Shrugs Unlimited.
A bar: Chugs Unlimited
Avatar: The Last Airbender tie-in merchandise store: Aangs Unlimited