Wood putty is quick drying, sandable and available in a wide range of colors. Select putty to match the wood type of your chaise, such as cherry, oak, walnut, teak or mahogany. Buy neutral putty and add universal colorant to achieve custom colors.
Custom mixing can give better color match, but is messier and time consuming. Tubes of ready-mixed filler are convenient for small repairs and can be applied direct from the nozzle. Some products contain oils that can discolor surrounding wood.
Coat holes in polyurethane first to avoid discoloration from oils.
Buy stainable wood filler and tint it yourself with wood stain. Check packaging to ascertain whether to mix stain into the putty before use, or to stain after hardening. Epoxy wood re-builder is a harder product that can be molded to replicate damaged carvings. Select an epoxy that is stainable.
Tim Carter recommends mixing different pre-colored putties to get the right tone, filling the hole only part way at first to check the color match.