Brooklyn appraisals

We kinda got screwed last year when the appraisal came back 50K less than asking, and the deal fell through. We were out almost $1,000 in fees up to that point. Now we've found a place again, but since we viewed it without a buyers agent, we are in negotiations on our own. Tried to find comps, but its difficult just looking online without an agent. They rejected our first two offers, without countering. We're able to pay up to asking, but don't want to be in the same boat with a low appraisal (we can only put down 10%, so it really has to come in spot on). Any suggestions???