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You can definitely make an offer with a contingency for sellers to pay closing costs. Doesn't mean that they will accept it, or they may counter by offering to pay up to a certain amount of them.
Depending on how much down you have (do you have 3.5% as would be typical for FHA? 10%? 20%?). If you have in excess of 3.5% for down payment, you might look into programs where the down payment requirement is less (i.e., FHA 3.5% or USDA as little as 0% down) to see if you qualify.