Just run a full node of whatever coin you want to accept and use the json-rpc interface... generate a new address for each client and keep a database that connects the client to the address...

Coins using the bitcoin codebase use more or less the same json rpc commands, coding something like this should be fairly simple... Altough i would advise to let a senior dev assist you... A simple mistake can have serious consequences, altough, as long as you keep your wallet locked, it should be fairly safe.