Most bike shops sell small rubber-coated clamps which you can wrap around your stays. I used two of these to mount a Blackburn Mountain Rack on my eyelet-less Schwinn KOM-10, and I mounted the one on the right immediately above the chain hanger, to prevent slippage. This arrangement has served me well for several years.
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"Far and away the best prize that life offers is the chance to work hard at work worth doing." --Theodore Roosevelt
Capo: 1959 Modell Campagnolo, S/N 40324; 1960 Sieger (2), S/N 42624, 42597
Carlton: 1962 Franco Suisse, S/N K7911
Peugeot: 1970 UO-8, S/N 0010468
Bianchi: 1982 Campione d'Italia, S/N 1.M9914
Schwinn: 1988 Project KOM-10, S/N F804069